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Adiabatic theorem

The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows:
 * A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum.

In simpler terms, a quantum mechanical system subjected to gradually changing external conditions adapts its functional form, but when subjected to rapidly varying conditions there is insufficient time for the functional form to adapt, so the spatial probability density remains unchanged.

Adiabatic pendulum
At the 1911 Solvay conference, Einstein gave a lecture on the quantum hypothesis, which states that $$E = nh \nu$$ for atomic oscillators. After Einstein's lecture, Hendrik Lorentz commented that, classically, if a simple pendulum is shortened by holding the wire between two fingers and sliding down, it seems that its energy will change smoothly as the pendulum is shortened. This seems to show that the quantum hypothesis is invalid for macroscopic systems, and if macroscopic systems do not follow the quantum hypothesis, then as the macroscopic system becomes microscopic, it seems the quantum hypothesis would be invalidated. Einstein replied that although both the energy $$E$$ and the frequency $$\nu$$ would change, their ratio $$\frac{E}{\nu}$$ would still be conserved, thus saving the quantum hypothesis.

Before the conference, Einstein had just read a paper by Paul Ehrenfest on the adiabatic hypothesis. We know that he had read it because he mentioned it in a letter to Michele Besso written before the conference.

Diabatic vs. adiabatic processes
At some initial time $$t_0$$ a quantum-mechanical system has an energy given by the Hamiltonian $$\hat{H}(t_0)$$; the system is in an eigenstate of $$\hat{H}(t_0)$$ labelled $$\psi(x,t_0)$$. Changing conditions modify the Hamiltonian in a continuous manner, resulting in a final Hamiltonian $$\hat{H}(t_1)$$ at some later time $$t_1$$. The system will evolve according to the time-dependent Schrödinger equation, to reach a final state $$\psi(x,t_1)$$. The adiabatic theorem states that the modification to the system depends critically on the time $$\tau = t_1 - t_0$$ during which the modification takes place.

For a truly adiabatic process we require $$\tau \to \infty$$; in this case the final state $$\psi(x,t_1)$$ will be an eigenstate of the final Hamiltonian $$\hat{H}(t_1) $$, with a modified configuration:

 * $$|\psi(x,t_1)|^2 \neq |\psi(x,t_0)|^2 .$$

The degree to which a given change approximates an adiabatic process depends on both the energy separation between $$\psi(x,t_0)$$ and adjacent states, and the ratio of the interval $$\tau$$ to the characteristic timescale of the evolution of $$\psi(x,t_0)$$ for a time-independent Hamiltonian, $$\tau_{int} = 2\pi\hbar/E_0$$, where $$E_0$$ is the energy of $$\psi(x,t_0)$$.

Conversely, in the limit $$\tau \to 0$$ we have infinitely rapid, or diabatic passage; the configuration of the state remains unchanged:

 * $$|\psi(x,t_1)|^2 = |\psi(x,t_0)|^2 .$$

The so-called "gap condition" included in Born and Fock's original definition given above refers to a requirement that the spectrum of $$\hat{H}$$ is discrete and nondegenerate, such that there is no ambiguity in the ordering of the states (one can easily establish which eigenstate of $$\hat{H}(t_1)$$ corresponds to $$\psi(t_0)$$). In 1999 J. E. Avron and A. Elgart reformulated the adiabatic theorem to adapt it to situations without a gap.

Comparison with the adiabatic concept in thermodynamics
The term "adiabatic" is traditionally used in thermodynamics to describe processes without the exchange of heat between system and environment (see adiabatic process), more precisely these processes are usually faster than the timescale of heat exchange. (For example, a pressure wave is adiabatic with respect to a heat wave, which is not adiabatic.) Adiabatic in the context of thermodynamics is often used as a synonym for fast process.

The classical and quantum mechanics definition is instead closer to the thermodynamical concept of a quasistatic process, which are processes that are almost always at equilibrium (i.e. that are slower than the internal energy exchange interactions time scales, namely a "normal" atmospheric heat wave is quasi-static, and a pressure wave is not). Adiabatic in the context of mechanics is often used as a synonym for slow process.

In the quantum world adiabatic means for example that the time scale of electrons and photon interactions is much faster or almost instantaneous with respect to the average time scale of electrons and photon propagation. Therefore, we can model the interactions as a piece of continuous propagation of electrons and photons (i.e. states at equilibrium) plus a quantum jump between states (i.e. instantaneous).

The adiabatic theorem in this heuristic context tells essentially that quantum jumps are preferably avoided, and the system tries to conserve the state and the quantum numbers.

The quantum mechanical concept of adiabatic is related to adiabatic invariant, it is often used in the old quantum theory and has no direct relation with heat exchange.

Simple pendulum
As an example, consider a pendulum oscillating in a vertical plane. If the support is moved, the mode of oscillation of the pendulum will change. If the support is moved sufficiently slowly, the motion of the pendulum relative to the support will remain unchanged. A gradual change in external conditions allows the system to adapt, such that it retains its initial character. The detailed classical example is available in the Adiabatic invariant page and here.

Quantum harmonic oscillator

The classical nature of a pendulum precludes a full description of the effects of the adiabatic theorem. As a further example consider a quantum harmonic oscillator as the spring constant $$k$$ is increased. Classically this is equivalent to increasing the stiffness of a spring; quantum-mechanically the effect is a narrowing of the potential energy curve in the system Hamiltonian.

If $$k$$ is increased adiabatically $\left(\frac{dk}{dt} \to 0\right)$ then the system at time $$t$$ will be in an instantaneous eigenstate $$\psi(t)$$ of the current Hamiltonian $$\hat{H}(t)$$, corresponding to the initial eigenstate of $$\hat{H}(0)$$. For the special case of a system like the quantum harmonic oscillator described by a single quantum number, this means the quantum number will remain unchanged. Figure 1 shows how a harmonic oscillator, initially in its ground state, $$n = 0$$, remains in the ground state as the potential energy curve is compressed; the functional form of the state adapting to the slowly varying conditions.

For a rapidly increased spring constant, the system undergoes a diabatic process $\left(\frac{dk}{dt} \to \infty\right)$ in which the system has no time to adapt its functional form to the changing conditions. While the final state must look identical to the initial state $$\left(|\psi(t)|^2 = |\psi(0)|^2\right)$$ for a process occurring over a vanishing time period, there is no eigenstate of the new Hamiltonian, $$\hat{H}(t)$$, that resembles the initial state. The final state is composed of a linear superposition of many different eigenstates of $$\hat{H}(t)$$ which sum to reproduce the form of the initial state.

Avoided curve crossing

For a more widely applicable example, consider a 2-level atom subjected to an external magnetic field. The states, labelled $$|1\rangle$$ and $$|2\rangle$$ using bra–ket notation, can be thought of as atomic angular-momentum states, each with a particular geometry. For reasons that will become clear these states will henceforth be referred to as the diabatic states. The system wavefunction can be represented as a linear combination of the diabatic states:

 * $$|\Psi\rangle = c_1(t)|1\rangle + c_2(t)|2\rangle.$$

With the field absent, the energetic separation of the diabatic states is equal to $$\hbar\omega_0$$; the energy of state $$|1\rangle$$ increases with increasing magnetic field (a low-field-seeking state), while the energy of state $$|2\rangle$$ decreases with increasing magnetic field (a high-field-seeking state). Assuming the magnetic-field dependence is linear, the Hamiltonian matrix for the system with the field applied can be written

 * $$\mathbf{H} = \begin{pmatrix}

\mu B(t)-\hbar\omega_0/2 & a \\ a^* & \hbar\omega_0/2-\mu B(t) \end{pmatrix}$$

where $$\mu$$ is the magnetic moment of the atom, assumed to be the same for the two diabatic states, and $$a$$ is some time-independent coupling between the two states. The diagonal elements are the energies of the diabatic states ($$E_1(t)$$ and $$E_2(t)$$), however, as $$\mathbf{H}$$ is not a diagonal matrix, it is clear that these states are not eigenstates of $$\mathbf{H}$$ due to the off-diagonal coupling constant.

The eigenvectors of the matrix $$\mathbf{H}$$ are the eigenstates of the system, which we will label $$|\phi_1(t)\rangle$$ and $$|\phi_2(t)\rangle$$, with corresponding eigenvalues $$\begin{align} \varepsilon_1(t) &= -\frac{1}{2}\sqrt{4a^2 + (\hbar\omega_0 - 2\mu B(t))^2} \\[4pt] \varepsilon_2(t) &= +\frac{1}{2}\sqrt{4a^2 + (\hbar\omega_0 - 2\mu B(t))^2}. \end{align}$$

It is important to realise that the eigenvalues $$\varepsilon_1(t)$$ and $$\varepsilon_2(t)$$ are the only allowed outputs for any individual measurement of the system energy, whereas the diabatic energies $$E_1(t)$$ and $$E_2(t)$$ correspond to the expectation values for the energy of the system in the diabatic states $$|1\rangle$$ and $$|2\rangle$$.

Figure 2 shows the dependence of the diabatic and adiabatic energies on the value of the magnetic field; note that for non-zero coupling the eigenvalues of the Hamiltonian cannot be degenerate, and thus we have an avoided crossing. If an atom is initially in state $$|\phi_2(t_0)\rangle$$ in zero magnetic field (on the red curve, at the extreme left), an adiabatic increase in magnetic field $\left(\frac{dB}{dt} \to 0\right)$ will ensure the system remains in an eigenstate of the Hamiltonian $$|\phi_2(t)\rangle$$ throughout the process (follows the red curve). A diabatic increase in magnetic field $\left(\frac{dB}{dt}\to \infty\right)$ will ensure the system follows the diabatic path (the dotted blue line), such that the system undergoes a transition to state $$|\phi_1(t_1)\rangle$$. For finite magnetic field slew rates $\left(0 < \frac{dB}{dt} < \infty\right)$ there will be a finite probability of finding the system in either of the two eigenstates. See below for approaches to calculating these probabilities.

These results are extremely important in atomic and molecular physics for control of the energy-state distribution in a population of atoms or molecules.

Mathematical statement
Under a slowly changing Hamiltonian $$H(t)$$ with instantaneous eigenstates $$| n(t) \rangle$$ and corresponding energies $$E_n(t)$$, a quantum system evolves from the initial state $$| \psi(0) \rangle = \sum_n c_n(0) | n(0) \rangle$$ to the final state $$| \psi(t) \rangle = \sum_n c_n(t) | n(t) \rangle ,$$ where the coefficients undergo the change of phase $$c_n(t) = c_n(0) e^{i \theta_n(t)} e^{i \gamma_n(t)}$$

with the dynamical phase $$\theta_m(t) = -\frac{1}{\hbar} \int_0^t E_m(t') dt'$$

and geometric phase $$\gamma_m(t) = i \int_0^t \langle m(t') | \dot{m}(t') \rangle dt' .$$

In particular, $$|c_n(t)|^2 = |c_n(0)|^2$$, so if the system begins in an eigenstate of $$H(0)$$, it remains in an eigenstate of $$H(t)$$ during the evolution with a change of phase only.

Proofs

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!Sakurai in Modern Quantum Mechanics This proof is partly inspired by one given by Sakurai in Modern Quantum Mechanics. The instantaneous eigenstates $$| n(t) \rangle$$ and energies $$E_n(t)$$, by assumption, satisfy the time-independent Schrödinger equation $$H(t) | n(t) \rangle = E_n(t) | n(t) \rangle$$ at all times $$t$$. Thus, they constitute a basis that can be used to expand the state $$| \psi(t) \rangle = \sum_n c_n(t) | n(t) \rangle$$ at any time $$t$$. The evolution of the system is governed by the time-dependent Schrödinger equation $$i \hbar |\dot{\psi}(t) \rangle = H(t) | \psi(t) \rangle,$$ where $$\dot{} = d / dt$$ (see ). Insert the expansion of $$| \psi(t) \rangle$$, use $$H(t) | n(t) \rangle = E_n(t) | n(t) \rangle$$, differentiate with the product rule, take the inner product with $$| m(t) \rangle$$ and use orthonormality of the eigenstates to obtain $$i \hbar \dot{c}_m(t) + i \hbar \sum_n c_n(t) \langle m(t) | \dot{n}(t) \rangle = c_m(t) E_m(t) .$$

This coupled first-order differential equation is exact and expresses the time-evolution of the coefficients in terms of inner products $$\langle m(t) | \dot{n} (t) \rangle$$ between the eigenstates and the time-differentiated eigenstates. But it is possible to re-express the inner products for $$m \neq n$$ in terms of matrix elements of the time-differentiated Hamiltonian $$\dot{H}(t)$$. To do so, differentiate both sides of the time-independent Schrödinger equation with respect to time using the product rule to get $$\dot{H}(t)|n(t)\rangle + H(t)|\dot{n}(t)\rangle = \dot{E}_n(t) |n(t)\rangle + E_n(t) |\dot{n}(t)\rangle .$$

Again take the inner product with $$| m(t) \rangle$$ and use $$\langle m(t) | H(t) = E_m(t) \langle m(t) |$$ and orthonormality to find $$\langle m(t) | \dot{n}(t) \rangle = - \frac{\langle m(t) | \dot{H}(t) | n(t) \rangle}{E_m(t) - E_n(t)} \qquad (m \neq n).$$

Insert this into the differential equation for the coefficients to obtain $$\dot{c}_m(t) + \left(\frac{i}{\hbar} E_m(t) + \langle m(t) | \dot{m}(t) \rangle \right) c_m(t) = \sum_{n \neq m} \frac{\langle m(t) | \dot{H} | n(t) \rangle}{E_m(t) - E_n(t)} c_n(t).$$

This differential equation describes the time-evolution of the coefficients, but now in terms of matrix elements of $$\dot{H}(t)$$. To arrive at the adiabatic theorem, neglect the right hand side. This is valid if the rate of change of the Hamiltonian $$\dot{H}(t)$$ is small and there is a finite gap $$E_m(t) - E_n(t) \neq 0$$ between the energies. This is known as the adiabatic approximation. Under the adiabatic approximation, $$\dot{c}_m(t) = i \left(-\frac{E_m(t)}{\hbar} + i \langle m(t) | \dot{m}(t) \rangle \right) c_m(t)$$ which integrates precisely to the adiabatic theorem $$c_m(t) = c_m(0) e^{i \theta_m(t)} e^{i \gamma_m(t)}$$ with the phases defined in the statement of the theorem.

The dynamical phase $$\theta_m(t)$$ is real because it involves an integral over a real energy. To see that the geometric phase $$\gamma_m(t)$$ is purely real, differentiate the normalization $$\langle m(t) | m(t) \rangle = 1$$ of the eigenstates and use the product rule to find that

$$0 = \frac{d}{dt} \Bigl ( \langle m(t) | m(t) \rangle \Bigr ) = \langle \dot{m}(t) | m(t) \rangle + \langle m(t)) | \dot{m}(t) \rangle = \langle m(t)) | \dot{m}(t) \rangle^* + \langle m(t)) | \dot{m}(t) \rangle = 2 \, \operatorname{Re} \Bigl ( \langle m(t)) | \dot{m}(t) \rangle \Bigr ) . $$

Thus, $$\langle m(t)) | \dot{m}(t) \rangle $$ is purely imaginary, so the geometric phase $$\gamma_m(t) $$ is purely real.
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!Adiabatic approximation Proof with the details of the adiabatic approximation We are going to formulate the statement of the theorem as follows:

 * For a slowly varying Hamiltonian $$\hat{H}$$ in the time range T the solution of the schroedinger equation $$\Psi(t)$$ with initial conditions $$\Psi(0) = \psi_{n}(0)$$
 * where $$\psi_{n}(t)$$ is the eigenvector of the instantaneous Schroedinger equation $$\hat{H}(t)\psi_{n}(t)=E_{n}(t)\psi_{n}(t)$$ can be approximated as: $$\left\| {\Psi(t)-\psi_\text{adiabatic}(t)} \right\| \approx O(\frac{1}{T})$$ where the adiabatic approximation is: $$ |\psi_\text{adiabatic}(t)\rangle = e^{i\theta_{n}(t)}e^{i\gamma_{n}(t)}|\psi_n(t)\rangle$$ and $$\theta_{n}(t) = - \frac{1}{\hbar} \int_{0}^{t}E_{n}(t') dt'$$ $$\gamma_{n}(t) = \int_{0}^{t}\nu_{n}(t')dt'$$ also called Berry phase $$\nu_{n}(t) = i \langle\psi_{n}(t) | \dot{\psi}_{n}(t)\rangle$$

And now we are going to prove the theorem.

Consider the time-dependent Schrödinger equation $$i \hbar{\partial \over \partial t} |\psi(t)\rangle = \hat{H}(\tfrac{t}{T}) |\psi(t)\rangle$$ with Hamiltonian $$\hat{H}(t).$$ We would like to know the relation between an initial state $$|\psi(0)\rangle$$ and its final state $$|\psi(T)\rangle$$ at $$t = T$$ in the adiabatic limit $$T \to \infty.$$

First redefine time as $$\lambda = \tfrac{t}{T} \in [0,1]$$: $$i \hbar{\partial \over \partial \lambda} |\psi(\lambda)\rangle = T \hat{H}(\lambda) |\psi(\lambda)\rangle.$$ At every point in time $$\hat{H}(\lambda)$$ can be diagonalized $$\hat H(\lambda)|\psi_n(\lambda)\rangle = E_n(\lambda)|\psi_n(\lambda)\rangle$$ with eigenvalues $$E_n$$ and eigenvectors $$|\psi_n(\lambda)\rangle$$. Since the eigenvectors form a complete basis at any time we can expand $$|\psi(\lambda)\rangle$$ as: $$ |\psi(\lambda)\rangle = \sum_n c_n(\lambda)|\psi_n(\lambda)\rangle e^{iT\theta_n(\lambda)},$$ where $$\theta_n(\lambda) = -\frac{1}{\hbar}\int_0^\lambda E_n(\lambda')d\lambda'.$$ The phase $$\theta_n(t)$$ is called the dynamic phase factor. By substitution into the Schrödinger equation, another equation for the variation of the coefficients can be obtained: $$i \hbar \sum_n (\dot{c}_n|\psi_n\rangle + c_n|\dot{\psi}_n\rangle + i c_n|\psi_n\rangle T\dot{\theta}_n)e^{iT\theta_n} = \sum_n c_n T E_n|\psi_n\rangle e^{iT\theta_n}.$$ The term $$\dot{\theta}_n$$ gives $$-E_n/\hbar$$, and so the third term of left side cancels out with the right side, leaving $$\sum_n \dot{c}_n|\psi_n\rangle e^{iT\theta_n} = -\sum_n c_n|\dot{\psi}_n\rangle e^{iT\theta_n}.$$

Now taking the inner product with an arbitrary eigenfunction $$\langle\psi_m|$$, the $$\langle\psi_m|\psi_n\rangle$$ on the left gives $$\delta_{nm}$$, which is 1 only for m = n and otherwise vanishes. The remaining part gives $$\dot{c}_m = -\sum_n c_n\langle\psi_m|\dot{\psi}_n\rangle e^{iT(\theta_n-\theta_m)}.$$

For $$T \to \infty$$ the $$e^{iT(\theta_n-\theta_m)}$$ will oscillate faster and faster and intuitively will eventually suppress nearly all terms on the right side. The only exceptions are when $$\theta_n-\theta_m$$ has a critical point, i.e. $$E_n(\lambda) = E_m(\lambda)$$. This is trivially true for $$m = n$$. Since the adiabatic theorem assumes a gap between the eigenenergies at any time this cannot hold for $$m \neq n$$. Therefore, only the $$m = n$$ term will remain in the limit $$T \to \infty$$.

In order to show this more rigorously we first need to remove the $$m = n$$ term. This can be done by defining $$d_m(\lambda) = c_m(\lambda) e^{\int_0^\lambda\langle\psi_m|\dot{\psi}_m\rangle d\lambda} = c_m(\lambda) e^{-i\gamma_m(\lambda)}.$$

We obtain: $$\dot{d}_m = -\sum_{n\neq m} d_n\langle\psi_m|\dot{\psi}_n\rangle e^{iT(\theta_n-\theta_m)-i(\gamma_m-\gamma_n)}.$$ This equation can be integrated: $$\begin{align} d_m(1)-d_m(0) &= -\int_0^1 \sum_{n\neq m} d_n\langle\psi_m|\dot{\psi}_n\rangle e^{iT(\theta_n-\theta_m)-i(\gamma_m-\gamma_n)} d\lambda\\ &= -\int_0^1 \sum_{n\neq m} (d_n-d_n(0))\langle\psi_m|\dot{\psi}_n\rangle e^{iT(\theta_n-\theta_m)-i(\gamma_m-\gamma_n)} d\lambda - \int_0^1 \sum_{n\neq m} d_n(0)\langle\psi_m|\dot{\psi}_n\rangle e^{iT(\theta_n-\theta_m)-i(\gamma_m-\gamma_n)}d\lambda \end{align}$$ or written in vector notation $$\vec{d}(1)-\vec{d}(0) = -\int_0^1 \hat{A}(T, \lambda) (\vec{d}(\lambda)-\vec{d}(0)) d\lambda - \vec{\alpha}(T).$$ Here $$\hat{A}(T, \lambda)$$ is a matrix and $$\alpha_m(T) = \int_0^1 \sum_{n\neq m} d_n(0)\langle\psi_m|\dot{\psi}_n\rangle e^{iT(\theta_n-\theta_m)- i(\gamma_m-\gamma_n)}d\lambda$$ is basically a Fourier transform. It follows from the Riemann-Lebesgue lemma that $$\vec{\alpha}(T) \to 0 $$ as $$T \to \infty$$. As last step take the norm on both sides of the above equation: $$\Vert\vec{d}(1)- \vec{d}(0)\Vert \leq \Vert\vec{\alpha}(T)\Vert + \int_0^1 \Vert\hat{A}(T, \lambda)\Vert \Vert\vec{d}(\lambda)-\vec{d}(0)\Vert d\lambda$$ and apply Grönwall's inequality to obtain $$\Vert\vec{d}(1)-\vec{d}(0)\Vert \leq \Vert\vec{\alpha}(T)\Vert e^{\int_0^1 \Vert\hat{A}(T, \lambda)\Vert d\lambda}.$$ Since $$\vec{\alpha}(T) \to 0$$ it follows $$\Vert\vec{d}(1)-\vec{d}(0)\Vert \to 0$$ for $$T \to \infty$$. This concludes the proof of the adiabatic theorem.

In the adiabatic limit the eigenstates of the Hamiltonian evolve independently of each other. If the system is prepared in an eigenstate $$|\psi(0)\rangle = |\psi_n(0)\rangle$$ its time evolution is given by: $$|\psi(\lambda)\rangle = |\psi_n(\lambda)\rangle e^{iT\theta_n(\lambda)}e^{i \gamma_n(\lambda)}.$$

So, for an adiabatic process, a system starting from nth eigenstate also remains in that nth eigenstate like it does for the time-independent processes, only picking up a couple of phase factors. The new phase factor $$\gamma_n(t)$$ can be canceled out by an appropriate choice of gauge for the eigenfunctions. However, if the adiabatic evolution is cyclic, then $$\gamma_n(t)$$ becomes a gauge-invariant physical quantity, known as the Berry phase.
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!Generic proof in parameter space Let's start from a parametric Hamiltonian $$H(\vec{R}(t))$$, where the parameters are slowly varying in time, the definition of slow here is defined essentially by the distance in energy by the eigenstates (through the uncertainty principle, we can define a timescale that shall be always much lower than the time scale considered).

This way we clearly also identify that while slowly varying the eigenstates remains clearly separated in energy (e.g. also when we generalize this to the case of bands as in the TKNN formula the bands shall remain clearly separated). Given they do not intersect the states are ordered and in this sense this is also one of the meanings of the name topological order.

We do have the instantaneous Schrödinger equation: $$H(\vec{R}(t))| \psi_m(t)\rangle = E_m(t)| \psi_m(t)\rangle $$ And instantaneous eigenstates: $$\langle\psi_m(t)|\psi_n(t)\rangle = \delta_{mn}$$ The generic solution: $$\Psi(t) = \sum a_n(t)|\psi_n(t)\rangle$$ plugging in the full Schrödinger equation and multiplying by a generic eigenvector: $$\langle \psi_m(t)|i\hbar\partial_t|\Psi(t)\rangle = \langle \psi_m(t)|H(\vec{R}(t))|\Psi(t)\rangle $$ $$\dot{a}_m + \sum_n\langle \psi_m(t)|\partial_{\vec{R}} |\psi_n(t)\rangle\dot{\vec{R}}a_n = -\frac{i}{\hbar}E_m(t)a_m $$ And if we introduce the adiabatic approximation: $$ | \langle \psi_m(t)|\partial_{\vec{R}} |\psi_n(t)\rangle\dot{\vec{R}}a_n | \ll |a_m|$$ for each $$m\ne n$$ We have $$\dot{a}_m = - \langle \psi_m(t)|\partial_{\vec{R}} |\psi_m(t)\rangle\dot{\vec{R}}a_m -\frac{i}{\hbar}E_m(t)a_m$$ and $$a_m(t) = e^{-\frac{i}{\hbar} \int_{t_0}^t E_m(t')dt'} e^{i\gamma_m(t)}a_m(t_0)$$ where $$\gamma_m(t) = i \int_{t_0}^t \langle \psi_m(t)|\partial_{\vec{R}} |\psi_m(t)\rangle\dot{\vec{R}}dt' = i \int_C \langle \psi_m(\vec{R})|\partial_{\vec{R}} |\psi_m(\vec{R})\rangle d\vec{R} $$ And C is the path in the parameter space,

This is the same as the statement of the theorem but in terms of the coefficients of the total wave function and its initial state.

Now this is slightly more general than the other proofs given we consider a generic set of parameters, and we see that the Berry phase acts as a local geometric quantity in the parameter space. Finally integrals of local geometric quantities can give topological invariants as in the case of the Gauss-Bonnet theorem. In fact if the path C is closed then the Berry phase persists to Gauge transformation and becomes a physical quantity.
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Example applications
Often a solid crystal is modeled as a set of independent valence electrons moving in a mean perfectly periodic potential generated by a rigid lattice of ions. With the Adiabatic theorem we can also include instead the motion of the valence electrons across the crystal and the thermal motion of the ions as in the Born–Oppenheimer approximation.

This does explain many phenomena in the scope of:
 * thermodynamics: Temperature dependence of specific heat, thermal expansion, melting
 * transport phenomena: the temperature dependence of electric resistivity of conductors, the temperature dependence of electric conductivity in insulators, Some properties of low temperature superconductivity
 * optics: optic absorption in the infrared for ionic crystals, Brillouin scattering, Raman scattering

Deriving conditions for diabatic vs adiabatic passage
We will now pursue a more rigorous analysis. Making use of bra–ket notation, the state vector of the system at time $$t$$ can be written

 * $$|\psi(t)\rangle = \sum_n c^A_n(t)e^{-iE_nt/\hbar}|\phi_n\rangle ,$$

where the spatial wavefunction alluded to earlier is the projection of the state vector onto the eigenstates of the position operator

 * $$\psi(x,t) = \langle x|\psi(t)\rangle .$$

It is instructive to examine the limiting cases, in which $$\tau$$ is very large (adiabatic, or gradual change) and very small (diabatic, or sudden change).

Consider a system Hamiltonian undergoing continuous change from an initial value $$\hat{H}_0$$, at time $$t_0$$, to a final value $$\hat{H}_1$$, at time $$t_1$$, where $$\tau = t_1 - t_0$$. The evolution of the system can be described in the Schrödinger picture by the time-evolution operator, defined by the integral equation

 * $$\hat{U}(t,t_0) = 1 - \frac{i}{\hbar}\int_{t_0}^t\hat{H}(t')\hat{U}(t',t_0)dt' ,$$

which is equivalent to the Schrödinger equation.

 * $$i\hbar\frac{\partial}{\partial t}\hat{U}(t,t_0) = \hat{H}(t)\hat{U}(t,t_0),$$

along with the initial condition $$\hat{U}(t_0,t_0) = 1$$. Given knowledge of the system wave function at $$t_0$$, the evolution of the system up to a later time $$t$$ can be obtained using

 * $$|\psi(t)\rangle = \hat{U}(t,t_0)|\psi(t_0)\rangle.$$

The problem of determining the adiabaticity of a given process is equivalent to establishing the dependence of $$\hat{U}(t_1,t_0)$$ on $$\tau$$.

To determine the validity of the adiabatic approximation for a given process, one can calculate the probability of finding the system in a state other than that in which it started. Using bra–ket notation and using the definition $$|0\rangle \equiv |\psi(t_0)\rangle$$, we have:

 * $$\zeta = \langle 0|\hat{U}^\dagger(t_1,t_0)\hat{U}(t_1,t_0)|0\rangle - \langle 0|\hat{U}^\dagger(t_1,t_0)|0\rangle\langle 0 | \hat{U}(t_1,t_0) | 0 \rangle.$$

We can expand $$\hat{U}(t_1,t_0)$$

 * $$\hat{U}(t_1,t_0) = 1 + {1 \over i\hbar} \int_{t_0}^{t_1}\hat{H}(t)dt + {1 \over (i\hbar)^2} \int_{t_0}^{t_1}dt' \int_{t_0}^{t'}dt \hat{H}(t')\hat{H}(t) + \cdots.$$

In the perturbative limit we can take just the first two terms and substitute them into our equation for $$\zeta$$, recognizing that

 * $${1 \over \tau}\int_{t_0}^{t_1}\hat{H}(t)dt \equiv \bar{H}$$

is the system Hamiltonian, averaged over the interval $$t_0 \to t_1$$, we have:

 * $$\zeta = \langle 0|(1 + \tfrac{i}{\hbar}\tau\bar{H})(1 - \tfrac{i}{\hbar}\tau\bar{H})|0\rangle - \langle 0|(1 + \tfrac{i}{\hbar}\tau\bar{H})|0\rangle \langle 0|(1 - \tfrac{i}{\hbar}\tau\bar{H})|0\rangle .$$

After expanding the products and making the appropriate cancellations, we are left with:

 * $$\zeta = \frac{\tau^2}{\hbar^2}\left(\langle 0|\bar{H}^2|0\rangle - \langle 0|\bar{H}|0\rangle\langle 0|\bar{H}|0\rangle\right) ,$$

giving

 * $$\zeta = \frac{\tau^2\Delta\bar{H}^2}{\hbar^2} ,$$

where $$\Delta\bar{H}$$ is the root mean square deviation of the system Hamiltonian averaged over the interval of interest.

The sudden approximation is valid when $$\zeta \ll 1$$ (the probability of finding the system in a state other than that in which is started approaches zero), thus the validity condition is given by

 * $$\tau \ll {\hbar \over \Delta\bar{H}} ,$$

which is a statement of the time-energy form of the Heisenberg uncertainty principle.

Diabatic passage
In the limit $$\tau \to 0$$ we have infinitely rapid, or diabatic passage:

 * $$\lim_{\tau \to 0}\hat{U}(t_1,t_0) = 1 .$$

The functional form of the system remains unchanged:

 * $$|\langle x|\psi(t_1)\rangle|^2 = \left|\langle x|\psi(t_0)\rangle\right|^2 .$$

This is sometimes referred to as the sudden approximation. The validity of the approximation for a given process can be characterized by the probability that the state of the system remains unchanged:

 * $$P_D = 1 - \zeta.$$

Adiabatic passage
In the limit $$\tau \to \infty$$ we have infinitely slow, or adiabatic passage. The system evolves, adapting its form to the changing conditions,

 * $$|\langle x|\psi(t_1)\rangle|^2 \neq |\langle x|\psi(t_0)\rangle|^2 .$$

If the system is initially in an eigenstate of $$\hat{H}(t_0)$$, after a period $$\tau$$ it will have passed into the corresponding eigenstate of $$\hat{H}(t_1)$$.

This is referred to as the adiabatic approximation. The validity of the approximation for a given process can be determined from the probability that the final state of the system is different from the initial state:

 * $$P_A = \zeta .$$

The Landau–Zener formula
In 1932 an analytic solution to the problem of calculating adiabatic transition probabilities was published separately by Lev Landau and Clarence Zener, for the special case of a linearly changing perturbation in which the time-varying component does not couple the relevant states (hence the coupling in the diabatic Hamiltonian matrix is independent of time).

The key figure of merit in this approach is the Landau–Zener velocity: $$v_\text{LZ} = {\frac{\partial}{\partial t}|E_2 - E_1| \over \frac{\partial}{\partial q}|E_2 - E_1|} \approx \frac{dq}{dt} ,$$ where $$q$$ is the perturbation variable (electric or magnetic field, molecular bond-length, or any other perturbation to the system), and $$E_1$$ and $$E_2$$ are the energies of the two diabatic (crossing) states. A large $$v_\text{LZ}$$ results in a large diabatic transition probability and vice versa.

Using the Landau–Zener formula the probability, $$P_{\rm D}$$, of a diabatic transition is given by

$$\begin{align} P_{\rm D} &= e^{-2\pi\Gamma}\\ \Gamma &= {a^2/\hbar \over \left|\frac{\partial}{\partial t}(E_2 - E_1)\right|} = {a^2/\hbar \over \left|\frac{dq}{dt}\frac{\partial}{\partial q}(E_2 - E_1)\right|}\\ &= {a^2 \over \hbar|\alpha|}\\ \end{align}$$

The numerical approach
For a transition involving a nonlinear change in perturbation variable or time-dependent coupling between the diabatic states, the equations of motion for the system dynamics cannot be solved analytically. The diabatic transition probability can still be obtained using one of the wide varieties of numerical solution algorithms for ordinary differential equations.

The equations to be solved can be obtained from the time-dependent Schrödinger equation:

$$i\hbar\dot{\underline{c}}^A(t) = \mathbf{H}_A(t)\underline{c}^A(t) ,$$

where $$\underline{c}^A(t)$$ is a vector containing the adiabatic state amplitudes, $$\mathbf{H}_A(t)$$ is the time-dependent adiabatic Hamiltonian, and the overdot represents a time derivative.

Comparison of the initial conditions used with the values of the state amplitudes following the transition can yield the diabatic transition probability. In particular, for a two-state system: $$P_D = |c^A_2(t_1)|^2$$ for a system that began with $$|c^A_1(t_0)|^2 = 1$$.

title: Adiabatic theorem


text:
User:Jengod/Leslie M. Shaw

Leslie Mortimer Shaw (November 2, 1848–March 28, 1932) was an American businessman, lawyer and politician.

Born in Morristown, Vermont, he became a lawyer and banker, and in 1898 became Governor of Iowa, serving until 1902. He then became United States Secretary of the Treasury under President Theodore Roosevelt in 1902, serving until 1907.

He was a candidate for the nomination of the Republican Party during the U.S. presidential election, 1908.

After leaving the Presidential Cabinet and public life he returned to banking, working in New York City.

He died in Washington, D.C. and is buried in Denison, Iowa.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Jengod/Leslie M. Shaw


text:
Discrete valuation ring

In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal.

This means a DVR is an integral domain R that satisfies any one of the following equivalent conditions:

 * 1) R is a local principal ideal domain, and not a field.
 * 2) R is a valuation ring with a value group isomorphic to the integers under addition.
 * 3) R is a local Dedekind domain and not a field.
 * 4) R is a Noetherian local domain whose maximal ideal is principal, and not a field.
 * 5) R is an integrally closed Noetherian local ring with Krull dimension one.
 * 6) R is a principal ideal domain with a unique non-zero prime ideal.
 * 7) R is a principal ideal domain with a unique irreducible element (up to multiplication by units).
 * 8) R is a unique factorization domain with a unique irreducible element (up to multiplication by units).
 * 9) R is Noetherian, not a field, and every nonzero fractional ideal of R is irreducible in the sense that it cannot be written as a finite intersection of fractional ideals properly containing it.
 * 10) There is some discrete valuation ν on the field of fractions K of R such that R = {0} $$ \cup $$ {x $$ \in $$ K : ν(x) ≥ 0}.

Localization of Dedekind rings
Let $$\mathbb{Z}_{(2)} := \{ z/n\mid z,n\in\mathbb{Z},\,\, n\text{ is odd}\}$$. Then, the field of fractions of $$\mathbb{Z}_{(2)}$$ is $$\mathbb{Q}$$. For any nonzero element $$r$$ of $$\mathbb{Q}$$, we can apply unique factorization to the numerator and denominator of r to write r as $2^{k} z⁄n$ where z, n, and k are integers with z and n odd. In this case, we define ν(r)=k. Then $$\mathbb{Z}_{(2)}$$ is the discrete valuation ring corresponding to ν. The maximal ideal of $$\mathbb{Z}_{(2)}$$ is the principal ideal generated by 2, i.e. $$2\mathbb{Z}_{(2)}$$, and the "unique" irreducible element (up to units) is 2 (this is also known as a uniformizing parameter). Note that $$\mathbb{Z}_{(2)}$$ is the localization of the Dedekind domain $$\mathbb{Z}$$ at the prime ideal generated by 2.

More generally, any localization of a Dedekind domain at a non-zero prime ideal is a discrete valuation ring; in practice, this is frequently how discrete valuation rings arise. In particular, we can define rings
 * $$\mathbb Z_{(p)}:=\left.\left\{\frac zn\,\right| z,n\in\mathbb Z,p\nmid n\right\}$$

for any prime p in complete analogy.

p-adic integers
The ring $$\mathbb{Z}_p$$ of p-adic integers is a DVR, for any prime $$p$$. Here $$p$$ is an irreducible element; the valuation assigns to each $$p$$-adic integer $$x$$ the largest integer $$k$$ such that $$p^k$$ divides $$x$$.

Formal power series
Another important example of a DVR is the ring of formal power series $$R = kT$$ in one variable $$T$$ over some field $$k$$. The "unique" irreducible element is $$T$$, the maximal ideal of $$R$$ is the principal ideal generated by $$T$$, and the valuation $$\nu$$ assigns to each power series the index (i.e. degree) of the first non-zero coefficient.

If we restrict ourselves to real or complex coefficients, we can consider the ring of power series in one variable that converge in a neighborhood of 0 (with the neighborhood depending on the power series). This is a discrete valuation ring. This is useful for building intuition with the Valuative criterion of properness.

Ring in function field
For an example more geometrical in nature, take the ring R = {f/g : f, g polynomials in R[X] and g(0) ≠ 0}, considered as a subring of the field of rational functions R(X) in the variable X. R can be identified with the ring of all real-valued rational functions defined (i.e. finite) in a neighborhood of 0 on the real axis (with the neighborhood depending on the function). It is a discrete valuation ring; the "unique" irreducible element is X and the valuation assigns to each function f the order (possibly 0) of the zero of f at 0. This example provides the template for studying general algebraic curves near non-singular points, the algebraic curve in this case being the real line.

Henselian trait
For a DVR $$R$$ it is common to write the fraction field as $$K = \text{Frac}(R)$$ and $$\kappa = R/\mathfrak{m}$$ the residue field. These correspond to the generic and closed points of $$S=\text{Spec}(R).$$ For example, the closed point of $$\text{Spec}(\mathbb{Z}_p)$$ is $$\mathbb{F}_p$$ and the generic point is $$\mathbb{Q}_p$$. Sometimes this is denoted as

\eta \to S \leftarrow s $$

where $$\eta$$ is the generic point and $$s$$ is the closed point.

Localization of a point on a curve
Given an algebraic curve $$(X,\mathcal{O}_X)$$, the local ring $$\mathcal{O}_{X,\mathfrak{p}}$$ at a smooth point $$\mathfrak{p}$$ is a discrete valuation ring, because it is a principal valuation ring. Note because the point $$\mathfrak{p}$$ is smooth, the completion of the local ring is isomorphic to the completion of the localization of $$\mathbb{A}^1$$ at some point $$\mathfrak{q}$$.

Uniformizing parameter
Given a DVR R, any irreducible element of R is a generator for the unique maximal ideal of R and vice versa. Such an element is also called a uniformizing parameter of R (or a uniformizing element, a uniformizer, or a prime element).

If we fix a uniformizing parameter t, then M=(t) is the unique maximal ideal of R, and every other non-zero ideal is a power of M, i.e. has the form (tk) for some k≥0. All the powers of t are distinct, and so are the powers of M. Every non-zero element x of R can be written in the form αtk with α a unit in R and k≥0, both uniquely determined by x. The valuation is given by ν(x) = kv(t). So to understand the ring completely, one needs to know the group of units of R and how the units interact additively with the powers of t.

The function v also makes any discrete valuation ring into a Euclidean domain.

Topology
Every discrete valuation ring, being a local ring, carries a natural topology and is a topological ring. We can also give it a metric space structure where the distance between two elements x and y can be measured as follows:
 * $$|x-y| = 2^{-\nu(x-y)}$$

(or with any other fixed real number > 1 in place of 2). Intuitively: an element z is "small" and "close to 0" iff its valuation ν(z) is large. The function |x-y|, supplemented by |0|=0, is the restriction of an absolute value defined on the field of fractions of the discrete valuation ring.

A DVR is compact if and only if it is complete and its residue field R/M is a finite field.

Examples of complete DVRs include For a given DVR, one often passes to its completion, a complete DVR containing the given ring that is often easier to study. This completion procedure can be thought of in a geometrical way as passing from rational functions to power series, or from rational numbers to the reals.
 * the ring of p-adic integers and
 * the ring of formal power series over any field

Returning to our examples: the ring of all formal power series in one variable with real coefficients is the completion of the ring of rational functions defined (i.e. finite) in a neighborhood of 0 on the real line; it is also the completion of the ring of all real power series that converge near 0. The completion of $$\Z_{(p)}=\Q \cap \Z_p$$ (which can be seen as the set of all rational numbers that are p-adic integers) is the ring of all p-adic integers Zp.

title: Discrete valuation ring


text:
1996 Pulitzer Prize

Winners of the Pulitzer Prizes for 1996 were:

Journalism awards

 * Beat reporting:
 * Bob Keeler of Newsday, Long Island, New York. For his detailed portrait of a progressive local Catholic parish and its parishioners.
 * Spot News Reporting:
 * Robert D. McFadden of The New York Times. For his highly skilled writing and reporting on deadline during the year.
 * Spot News Photography:
 * Charles Porter IV, a free-lancer. For his haunting photographs, taken after the Oklahoma City bombing and distributed by the Associated Press, showing a one-year-old victim handed to and then cradled by a local fireman.
 * Commentary:
 * E.R. Shipp of the New York Daily News. For her penetrating columns on race, welfare and other social issues.
 * Criticism:
 * Robert Campbell of The Boston Globe. For his knowledgeable writing on architecture.
 * Editorial Cartooning:
 * Jim Morin of the Miami Herald.
 * Editorial Writing:
 * Robert B. Semple, Jr. of The New York Times. For his editorials on environmental issues.
 * Explanatory Reporting:
 * Laurie Garrett of Newsday, Long Island, New York. For her courageous reporting from Zaire on the Ebola virus outbreak there. (The winner was entered and nominated in the International Reporting category and was moved by the Pulitzer Prize Board to Explanatory Journalism.)
 * Feature Photography:
 * Stephanie Welsh, a free-lancer. For her shocking sequence of photos, published by Newhouse News Service, of a female genital cutting rite in Kenya.
 * Feature Writing:
 * Rick Bragg of The New York Times. For his elegantly written stories about contemporary America.
 * International Reporting:
 * David Rohde of The Christian Science Monitor. For his persistent on-site reporting of the massacre of thousands of Bosnian Muslims in Srebrenica.
 * Investigative Reporting:
 * Staff of the Orange County Register, Santa Ana, California. For reporting that uncovered fraudulent and unethical fertility practices at a leading research university hospital and prompted key regulatory reforms.
 * National Reporting:
 * Alix M. Freedman of The Wall Street Journal. For her coverage of the tobacco industry, including a report that exposed how ammonia additives heighten nicotine potency.
 * Public Service:
 * The News & Observer, Raleigh, North Carolina. For the work of Melanie Sill, Pat Stith and Joby Warrick on the environmental and health risks of waste disposal systems used in North Carolina's growing hog industry.

Letters, Drama and Music Awards

 * Biography or Autobiography:
 * God: A Biography by Jack Miles (Alfred A. Knopf)
 * Fiction:
 * Independence Day by Richard Ford (Alfred A. Knopf)
 * General Non-Fiction:
 * The Haunted Land: Facing Europe's Ghosts After Communism by Tina Rosenberg (Random House)
 * History:
 * William Cooper's Town: Power and Persuasion on the Frontier of the Early American Republic by Alan Taylor (Alfred A. Knopf)
 * Poetry:
 * The Dream of the Unified Field by Jorie Graham (The Ecco Press)
 * Drama:
 * Rent by Jonathan Larson (Rob Weisbach Books/William Morrow)
 * Music:
 * Lilacs by George Walker (MMB Music)

Special Citations

 * Pulitzer Prize Special Citations and Awards
 * Herb Caen, local columnist of the San Francisco Chronicle, for his extraordinary and continuing contribution as a voice and conscience of his city.

title: 1996 Pulitzer Prize


text:
L. M. Shaw

Leslie Mortier Shaw (November 2, 1848 – March 28, 1932) was an American businessman, lawyer, and politician. He served as the 17th Governor of Iowa and was a Republican candidate in the 1908 United States presidential election.

Biography
Shaw was born in Morristown, Vermont, the son of Boardman O. Shaw and Louise Spaulding "Lovisa" Shaw. He attended Cornell College in 1874. Shaw married the former Alice Crenshaw on December 6, 1877, with whom he had three children.

He became a lawyer and banker, and, in 1898, became the 17th Governor of Iowa, serving until 1902. He then became the U.S. Secretary of the Treasury under President Theodore Roosevelt from 1902 to 1907.

Like his predecessor Secretary Lyman Gage, Shaw firmly believed that the Treasury should serve the money market in times of difficulty through the introduction of Treasury funds. To this end, Shaw bought back the government bonds from commercial banks that owned them, increased the number of government depository banks, and in 1902, he told the banks that they no longer needed to keep cash reserves against their holdings of public funds. The intended effect of these actions was to provide a more elastic currency which would then respond to the needs of the market. The government intervention in the money market reached its height with Shaw. He supported tariff theory according to the New York Times.

He resigned on March 3, 1907, to become a banker in New York City. He was a candidate for the Republican Party nomination during the U.S. presidential election in 1908.

After leaving the Presidential Cabinet and his public life, he returned to banking, working in New York City. Shaw died in Washington, D.C., and was buried in Oakland Cemetery in Denison, Iowa.

title: L. M. Shaw


text:
Tobias Matthay

Tobias Augustus Matthay (19 February 1858 – 15 December 1945) was an English pianist, teacher, and composer.

Biography
Matthay was born in Clapham, Surrey, in 1858 to parents who had come from northern Germany and eventually became naturalised British subjects. He entered London's Royal Academy of Music in 1871 and eight months later he received the first scholarship given to honour the knighthood of its principal, Sir William Sterndale Bennett. At the academy, Matthay studied composition under Sir William Sterndale Bennett and Arthur Sullivan, and piano with William Dorrell and Walter Macfarren. He served as a sub-professor there from 1876 to 1880, and became an assistant professor of pianoforte in 1880, before being promoted to professor in 1884. With Frederick Corder and John Blackwood McEwen, he co-founded the Society of British Composers in 1905. Matthay remained at the RAM until 1925, when he was forced to resign because McEwen—his former student who was then the academy's Principal—publicly attacked his teaching.

In 1903, after over a decade of observation, analysis, and experimentation, he published The Act of Touch, an encyclopedic volume that influenced piano pedagogy throughout the English-speaking world. So many students were soon in quest of his insights that two years later he opened the Tobias Matthay Pianoforte School, first in Oxford Street, then in 1909 relocating to Wimpole Street, where it remained for the next 30 years. The teachers there included his sister Dora. He soon became known for his teaching principles that stressed proper piano touch and analysis of arm movements. He wrote several additional books on piano technique that brought him international recognition, and in 1912 he published Musical Interpretation, a widely read book that analyzed the principles of effective musicianship. However, whilst acknowledging its importance, a later interpreter of Matthay's writing criticized its lack of clarity: The interminable repetitions, recapitulations, summaries, footnotes, all with a change of emphasis and as often as not with new names for the same thing, led enquirers into a maze from which only the clearest brain equipped with a dogged perseverance, could extricate itself.

Many of his pupils went on to define a school of 20th century English pianism, including Arthur Alexander, York Bowen, Norman Fraser, Myra Hess, Denise Lasimonne, Clifford Curzon, Harold Craxton, Moura Lympany, Gertrude Peppercorn, Irene Scharrer, Lilias Mackinnon, Guy Jonson, Vivian Langrish, Hope Squire, Eileen Joyce, jazz "syncopated" pianist Raie Da Costa, Harriet Cohen, Dorothy Howell, and the duo Bartlett and Robertson. He taught many Americans, including Ray Lev, Eunice Norton, and Lytle Powell, and he was also the teacher of Canadian pianist Harry Dean, English composer Arnold Bax and English conductor Ernest Read. In 1920, Hilda Hester Collens, who had studied under Matthay from 1910 to 1914, founded a music college in Manchester named the Matthay School of Music in his honour. It was later renamed the Northern School of Music, a predecessor institution of the Royal Northern College of Music.

His wife Jessie née Kennedy, whom he married in 1893, wrote a biography of her husband, published posthumously in 1945. She was a sister of Marjory Kennedy-Fraser. She was born in 1869 and died in 1937. Tobias Matthay died at his country home, High Marley, near Haslemere in 1945, aged 87.

Compositions
Matthay's larger scale compositions and virtuoso piano works were all written between the 1870s and 1890s before he focused instead on piano technique and teaching. They include two symphonies, some concert overtures and several piano concertante works. They were all forgotten for many years, resurfacing at a Sotheby's manuscript auction on 30 November 2006, won by the Royal Academy of Music.

Only the symphonic overture In May (1883) and the one movement Concert Piece in A minor for piano and orchestra (begun about 1883 and revised till about 1908) gained much contemporary attention. The Concert Piece became his most popular large scale work, although its London premiere at the Proms had to wait 25 years before its first performance, on 28 August 1909. The soloist was York Bowen. It was then performed at the Proms by Vivian Langrish in 1914, in 1919, and 1920 and again in 1925 by Matthay's student Betty Humby (who later became Betty Humby Beecham after she married Thomas Beecham). Myra Hess also performed it under Matthay's baton at Queen's Hall on 18 July 1922 in the presence of the King and Queen for the Royal Academy of Music Centennial Celebration.

Matthay also wrote chamber music (most notably the Piano Quartet, op.20 of 1882), a small number of songs, and a great deal of piano music. His 31 Variations and Derivations on an Original Theme for piano, written in 1891 and revised till 1918, was one of his last important early period works. Showing the influence of both Liszt and Wagner, it was considered harmonically daring when first composed. The work is in two parts, the second growing increasingly complex.

During and after the First World War Matthay returned to piano composition, but abandoned his previously complex style in favour of short character pieces closer in spirit to Schumann's pieces for children. In 1933 he recorded some of these, including Twilight Hills and Wind Sprites from the 1919 suite On Surrey Hills, op.30, as well as the older Prelude and the highly demanding "Bravura" from Studies in the Form of a Suite (1887).

A nearly complete collection of the published piano works is held at the International Piano Archives at the University of Maryland. It was donated by the late James Matthew Holloway from papers originally in the possession of the pianist and favourite Mathay student Denise Lassimonne (1903–1994), whom Matthay took in after the death of her father, later naming her his ward and heir Many of the scores contain corrections, editorial markings and comments by Matthay himself.

List of works
Orchestral
 * Concert Overture (1874)
 * Symphony in A minor (1874)
 * Piano Concerto in D minor (1874)
 * Scherzo for Orchestra in D minor (1875)
 * Concert Overture in C (1877)
 * Symphony (1878)
 * Reminiscences of Country Life, concert overture (1879)
 * Hero and Leander, scena for contralto and orchestra (1879)
 * In Summer, symphonic overture (aka Introduction and Allegro) (1880)
 * Andante for Orchestra (1881)
 * Concert Piece for Piano and Orchestra in D minor (1881)
 * In May, symphonic overture (1883)
 * Concert Piece for Piano and Orchestra in A minor (1895)

Chamber
 * Piano Quartet in F (1876)
 * Piano Quartet, op. 20 (1882, revised 1905, published 1906)
 * Piano Trio in F
 * Ballade for cello and piano, op.40 (1936)

Piano Works (selected)
 * Moods of a Moment, op.11 (1886, revised and published 1920) (ten pieces)
 * Love Phases, op.12 (1880, published 1912) (includes 'Doubts', 'Avowal', 'Response')
 * Studies in the form of a Suite op.16 (1887) (eight studies)
 * Elves, op.17 (1898, published 1911)
 * Con Imitazione, op. 18
 * Sketch-Book No 1 op.24 (includes 'May Morning', 'Terpsichore') (1914)
 * Sketch Book No 2, op.26 (1916)
 * 31 Variations and Derivations on an Original Theme op.28 (1891, published 1918)
 * Five Cameos, op. 29 (1919)
 * On Surrey Hills op.30 (1919), includes 'Twilight Hills', 'On Holiday', 'Night Shadows', 'Wind Sprites'
 * Three Lyric Studies, op.33 (1921)
 * Ballade in A minor, op. 39 (1926)
 * Five Miniatures, op.45

title: Tobias Matthay


text: Category:Priests

title: Category:Priests


text: Category:Castles in Belarus

title: Category:Castles in Belarus


text:
User:Jengod/William A. Richardson

William Adams Richardson (November 2, 1821–October 19, 1896) was an American judge and politician.

Born in Tyngsboro, Massachusetts, he graduated from Harvard University in 1843.

In 1873 he was appointed United States Secretary of the Treasury by President Ulysses S. Grant. He had served as an Assistant Treasury Secretary under his predecessor, George S. Boutwell. He served one year, from 1873 until 1874.

The post-war economy had expanded so quickly that commercial banks became nervous and began calling in their loans. As a result, in the summer of 1873 the money supply tightened drastically, causing the Panic of 1873. Richardson responded by issuing $26 million in greenbacks to meet the demand. The legality of his action was doubtful, but the Congress did not interfere and the crisis was eased. Such cycles of expansion and panic continued for the next thirty years, however, and were the basis for the creation of the Federal Reserve in 1913.

In his last months in office Richardson became embroiled in the "Sanborn Incident."

After leaving the Treasury, Richardson was appointed by Grant to served as a Justice and Chief Justice of the U.S. Court of Claims in Massachusetts from 1874 until his death in Washington D.C. in 1896.

title: User:Jengod/William A. Richardson


text: User talk:69.157.54.69

title: User talk:69.157.54.69


text:
Edward Brown (Manitoba politician)

Edward Brown (May 23, 1865 – February 8, 1947) was a Manitoba politician. He served briefly as leader of the Manitoba Liberal Party (1906–07), and was later a cabinet minister in Tobias Norris' government (1915–1922).

Life and career
Born in Gresham, Bruce County, Canada West, the son of Edward J. Brown, was educated in St. Catharines. In 1882, he began business as a merchant in Paisley. In 1888, Brown came to Portage la Prairie; he served as mayor there for six years. He married Esther Huston in 1893. In 1909, Brown moved to Winnipeg where he established a financial brokerage firm that he operated until 1942. He was also president of the Canada West Securities Corporation and of the British Northwestern Fire Insurance Company. In 1910, he was listed as one of Winnipeg's 19 millionaires.

Brown made his electoral debut in the provincial campaign of 1903, narrowly losing to Conservative Hugh Armstrong in Portage la Prairie. He subsequently became a leading organizer for the Liberals, and was acclaimed as party leader on March 28, 1906 (replacing Charles Mickle). He was again defeated by Armstrong in the election of 1907, however, and resigned as party leader shortly thereafter. Brown lost a third electoral contest in 1910, falling to Lendrum McMeans in Winnipeg South, 2545 votes to 2496.

Brown finally entered parliament in 1915, running in a deferred election in the northern riding of The Pas. The Liberal party led by Premier Tobias Norris had already won a landslide victory in the rest of the province, and Brown had joined the cabinet as Provincial Treasurer; perhaps not surprisingly, he was unopposed for his riding. Brown held his cabinet position until the Norris government was defeated in 1922. In the election of 1920, he fended off a weak challenge from Labour candidate A. Norgrove.

In 1922, Brown supported efforts to reunite the "Unionist" and "Laurier Liberal" factions of the Liberal Party in Canada and Manitoba (see Wilfrid Laurier). While these efforts were successful, they led to a popular perception that the previously-independent Norris government would henceforth be subservient to the federal Liberals. Opposition parties used this to their advantage in the election of 1922, which the United Farmers of Manitoba won in a landslide.

Brown was not a candidate in 1922, and did not return to political life thereafter.

He died in Winnipeg at the age of 81.

title: Edward Brown (Manitoba politician)


text:
VAD

VAD may refer to:

Physiology, medicine etc.

 * Vascular dementia (VaD), dementia caused by problems in the supply of blood to the brain
 * Vertebral artery dissection, the development of a flap-like tear in the vertebral artery
 * Ventricular assist device, a mechanical circulatory device used to replace the function of a failing heart
 * Vitamin A deficiency, a lack of vitamin A in humans
 * Vincristine, Adriamycin (doxorubicin), Dexamethasone; a chemotherapy regimen used for multiple myeloma
 * Voluntary assisted dying

Other

 * Voluntary Aid Detachment, a voluntary organisation providing field nursing services in the British Empire
 * VÄD (vodka), an American vodka
 * Voice activity detection, a technique in which the presence or absence of human speech is detected
 * Voice-Activated Dialling, speech recognition to identify the destination for a telephone call in interactive voice response
 * Velocity-Azimuth Display, a technique used to estimate vertical and horizontal components of atmospheric wind vectors from a radar

title: VAD


text:
User talk:Plumpy

Helping to fight vandalism
Thanks for removing vandalism from the Hyphy page. For future reference, you can click the history tab at the top of the page and revert to the first version that the user hasn't touched. It makes it easier to remove all the random vandalism that crops up. --Liface 18:14, 22 August 2006 (UTC)

Graduation Cover
The cover is real Sf2070 11:24, 26 July 2007 (UTC)

Notification: changes to "Mark my edits as minor by default" preference
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Thank you for your understanding and happy editing :) Editing on behalf of User:Jarry1250, LivingBot (talk) 17:04, 15 March 2011 (UTC)

title: User talk:Plumpy


text:
Moser

Moser may refer to:
 * Moser (surname)
 * An individual who commits the act of Mesirah in Judaism

Places

 * Moser Glacier, a glacier on the west coast of Graham Land, Antarctica
 * Moser River, Nova Scotia, Canada
 * Moser Bay Seaplane Base, a public-use seaplane base in Moser Bay, Alaska
 * Moser Channel, a passage spanned by the Seven Mile Bridge in the Florida Keys
 * Moser Farm, a historic farm near Kirschnerville, New York

Companies

 * Moser Baer, a technology company based in New Delhi, India
 * Moser Cicli, an Italian bicycle manufacturer
 * Moser (glass company), a Czech-based glass manufacturer
 * Moser's Rides, an Italian amusement ride manufacturer

title: Moser


text:
Talk:Drentse Patrijshond

Corrected colors
Fixed sentence regarding valid colors. Only valid color is white with brown or orange markings. First set of colors in first draft shouldn't have been there. Inadvertently left it in after cutting and pasting the text from another page. I used that as a template and forgot to wipe out that sentence.

Vic 02:04, 22 Jul 2004 (UTC)

Painting
I found one painting at the Rijksmuseum with a picture of what is clearly a "Dutch Partridge Dog" -- the man is handing the woman a partridge, which was apparently a double entendre at the time. The painting is The Hunter's Present, c. 1658-60, by Gabriel Metsu. The dog is large - large enough to imagine pulling a cart. I was wondering about that. --Hafwyn (talk) 18:51, 12 August 2008 (UTC)

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Magars

The Magars, also spelled Mangar and Mongar, are Magar language speaking ethnolinguistic group native to Nepal, representing 6.9% of Nepal's total population according to the 2021 Nepal census. They are one of the main Gurkha tribes.

The first home of the Magars was to the west of the Gandaki River and, roughly speaking, consisted of that portion of Nepal which lies between and around about Gulmi, Arghakhanchi, and Palpa. This part of the country was divided into twelve districts known as Bahra Magarat (Confederation of Twelve Magar villages), which included the following regions of that period: Argha, Khanchi, Bhirkot, Dhor, Garhung, Ghiring, Gulmi, Isma, Musikot, Rising, Satung, and Pyung. During the medieval period, the whole area from Palpa to Rukum Rolpa was called the Magarat, a place settled and inhabited by Magars. Another confederation of eighteen Magar kingdoms, known as Athara Magarat, also existed and was originally inhabited by Kham Magars.

Geographical distribution
At the time of the 2011 Nepal census, 1,887,733 people (7.1% of the population of Nepal) identified as Magar. The frequency of Magar people by province was as follows: The frequency of Magar people was higher than national average in the following districts:
 * Gandaki Province (19.0%)
 * Lumbini Province (15.1%)
 * Karnali Province (10.9%)
 * Bagmati Province (4.9%)
 * Koshi Province (4.2%)
 * Sudurpashchim Province (2.2%)
 * Madhesh Province (1.2%)
 * Palpa (52.6%)
 * Eastern Rukum (50.7%)
 * Rolpa (43.4%)
 * Myagdi (39.6%)
 * Pyuthan (32.7%)
 * Nawalpur (29.1%)
 * Baglung (28.1%)
 * Tanahun (27.1%)
 * Syangja (21.5%)
 * Gulmi (20.7%)
 * Surkhet (19.1%)
 * Arghakhanchi (18.0%)
 * Salyan (15.1%)
 * Sindhuli (14.8%)
 * Western Rukum (14.7%)
 * Udayapur (13.9%)
 * Dang (13.6%)
 * Dolpa (12.6%)
 * Gorkha (11.6%)
 * Okhaldhunga (11.3%)
 * Ramechhap (11.2%)
 * Parbat (11.0%)
 * Rupandehi (10.7%)
 * Dhankuta (9.7%)
 * Dailekh (9.2%)
 * Jajarkot (9.0%)
 * Kaski (8.6%)
 * Dhading (8.5%)
 * Mustang (7.9%)

Origin
There are several mythical stories describing the origins of the Magars.

The Magar of the Bahra Magarat east of the Kali Gandaki River are said to have originated in the land of Seem. Two brothers, Seem Magar and Chintoo Magar, fought, and one remained in Seem, while the other left, ending up in Kangwachen, southern Sikkim. The Bhutia people lived at the northern end of this region. Over time, the Magars became very powerful and made the northern Bhutia their vassals. Sintoo Sati Sheng ruled in a very despotic manner, and the Bhutia conspired to assassinate him. Sheng's queen took revenge and poisoned 1,000 Bhutia people at a place now called Tong Song Fong, meaning "where a thousand were murdered". The Bhutia later drove the Magars out, forcing them to again migrate further south. As part of this migration, one group migrated to Simrongadh, one group moved towards the Okhaldhunga region, and another group seems to have returned to the east. No dates are given.

The origins of the Kaike Magars end up with the mystical tales told and retold by local people. According to one of these stories, the Kaike Magars were the sons of a woman who had fled from an unspecified village of Kalyal kingdom. She subsequently gave birth to her child, a son. The boy, when he grew up, captured an angel while she was bathing with her friends. As time went by, the son and his angel bride had three sons. These sons were the ancestors of the Buddha, Roka, and Gharti clans. The origin of the fourth major clan is different. One of the three sons was a shepherd who kept losing the same female goat every day, so one day he followed her when she wandered away from the rest of the herd. He discovered that she was giving her milk to a baby boy living in the hollow part of a bamboo tree. He brought the baby home. This boy grew up and became the ancestor of the Jhankri clan. The language was called "Kaike," meaning "language of the Gods."

History
The first written history about the Magar people dates as far back as 1100 CE. The Magars are one of the oldest known tribes in Nepal. Their ancient homeland was known as Magwar Bisaya, later called Magarat.

Magarat bordered from Marsyangdi river to the Pyuthan area during that time. The Magars prospered at such a level during that period that this part of the country was divided into twelve kingdoms/thams (Barah Magarant or twelve magarat) —each under its own ruler—the members of each supposedly being of common extraction in the male line. Some records show these twelve areas as being Arghak, Khachi, Gulmi, Isma, Musikot, Ghiring, Rising, Bhirkot, Payung, Garhung, Dhor and Satung. Among them, the most powerful kings were those of Gulmi, Argha, Khachi. Broadly speaking, the twelve Magarat consisted of present-day Argha, Khanchi, Gulmi, Isma, Musikot, Ghiring, Baldengadhi, Rudrapurgadhi, Deuchuli, Tanahang/Tanu-hyula (Tanahu), Kanhu, Ligligkot, Gorkhakot, (Bahakot), Targhakot (Takukot), and Makawanpur areas. Similarly, Athara (eighteen) Magarat consisted of the following regions: Dhurkoi (Gulmi), Gharkoi (Arghakhachi), Paiya (Parbat), Sinkhang (Myagdi), Narikoi (Pyuthan), Balungbang (Pyuthan), Jangkoi (Rolpa), Rukumkoi (Rukum), Chhilikoi (Dang), Bhaba (Dailekh), Borekoi (Jajarkot), Tarakoi (Dolpa), Timarkoi (Jumla), Jural (Doti), Bunkot, Bahrakot, Lu Nanya (Dadeldhura) and Ru-pal (Dadeldhura).

The Magars of the middle and western regions also played an important role in Nepal's formative history. Their kingdom was one of the strongest of west Nepal in and around Palpa District during the time of the 22 Baisi Rajya and 24 Chaubisi Rajya  principalities (17th and early 18th centuries). In the 16th century, Palpa ruler Mukunda Sen briefly invaded the Kathmandu valley. Dravya Shah captured Gorkhakot, the last Magarat area, from the Magar King, Mansingh Khadka Magar in BS 1616 Bhadra 25. In the kingdoms of Gorkha and Musikot, the Magars even seem to have taken part in their own initial defeat, revealing both the weakness of their ethnic solidarity at that time and the presence of clan rivalries. As mentioned in the Journal of the Asiatic Society of Bengal founded by Sir William Jones in 1784, the city of Gorkha was originally the residence of Chitoria (Chitorey) Magars, and the city was built by them. To this day, large numbers of Chitoria/Chitorey Magars are found in the Gorkha District. Additionally, in the Manakamana Temple located in Gorkha, it is mandatory for a priest to be a Magar; specifically, the priest must be a descendant of Saint Lakhan Thapa Magar, who is described as a spiritual guide for Ram Shah, and he had a very close relationship with the queen, who was considered an incarnation of the Goddess. Interestingly, the main priests of Kalika, the goddess protecting the kingdoms of Lamjung and Gorkha, were also Bohara Magars; it is striking to note how the Magars have been in charge of the religious functions linked to the very source of Thakuri power.

The 18th-century king, Prithvi Narayan Shah, the founder of the modern Kingdom of Nepal announced and loved to call himself ' the King of Magarat' or 'the King of Magar country'. According to Marie Lecomte-Tilouine, a senior researcher in Social Anthropology at the French National Center for Scientific Research, Prithvi Narayan Shah narrated in his autobiography about praying to a goddess whom he described as 'the daughter of Rana [Magar]. During the time of King Prithvi Narayan, Rana Magars were one of the six-member courtiers (Tharghar). Prithvi Narayan Shah in his memories also recalls his Magar dada—the man who looked after him during his childhood.

The Scottish contemporary writer, Francis Buchanan-Hamilton, contends in his journal that the Shah dynasty was derived from the Magar tribe. He argues that: "The family of Gorkha or Gorkha Kingdom which now governs Nepal, although it pretends to come from Chittor, according to Sadhu Ram, a good authority, is, in reality, of the Magar tribe; and, at any rate, these people are now firmly attached to its interests, by having largely shared in the sweets of conquest; and by far the greatest part of the regular troops of that family is composed of this nation."

He further contended on Shah family that: "The family pretends to be of the Pamar tribe; but it is alleged, as I have already explained, that this is a mere fable, and that, on the arrival of the colony from Chitaur, this family were Magars."

Many prominent historians of Nepal have claimed that Aramudi, an eighth-century ruler of the Kali Gandaki region, was a Magar King. "Aramudi" derives from the word for 'river' in the Magar language. 'Ari' – 'Source of Water' + 'Modi'– 'River' = 'Arimodi' or 'Aramudi', thus the literal meaning of Aramudi is a source of river. But due to the lack of historical evidence, there are some conflicting ideas among the historians.

Sen dynasty of Palpa were Magar Kings as per the hand-written treatise 'Naradsmriti' and history books written in Sikkim. In a palm-leaf manuscript kept in the Kaiser Library, dated 1567 VS (1510), Mukunda Sen is described as a Magar king of Palpa who invaded the Kathmandu Valley in 1581 VS (1524). Thus, in the 17th century, Malla kings of Kathmandu valley were united to fight back the invasion of Magars from Palpa. One of Mukunda Sen's wives was also the daughter of the Magar King of Parkogha: Mahadevi Suvarnamala, and she had four sons: Manishya Sen, Imbarsen, Kuvar and Lohang Sen. Similarly, Gajalaxman Singh, Magar King of Makvanpur, whose daughter Kantivati was married to Abhaya Sen (Magar King) of Palpa. From her was born the great king of kings Bhattarajadeva. Around 1700, the ruler of Baldeng (near present-day Butwal) was overthrown by Palpa and other chaubisi states, and he was supposedly a Magar king.

Subdivisions
Magars are divided into the following Eight tribes (clans) listed here in an alphabetical order: Ale, Budha/Budhathoki, Chitorey/Chitaurey, Gharti, Pun, Rana, Roka, Thapa. These tribes all intermarry with each other, have the same customs, and are in every way equal as regards to social standing. Each tribe is subdivided into many sub-clans.

Chitorey/Chitaurey
Chitorey, Chitaurey

Ale Magars
Arghali, Durungchung, Hiski, Hungchen, Limel, Pade, Rakhal, Suyal, Sirpali.

Budhathoki / Budha Magars
Gamal, Jugjali, Pahari, Thami, Arkali, Ulange, Karmani, Kosila, Gamal, Chini, Jiyali, Thami, Janjali, Darlasi, Deowal, Namjali, Pare, Pahare, Pojange, Barkabiri, Balkoti, Ramjali, Romkhami, Sinjali/Singjali, Jujali, Lamichhane, Khame, Doyal.

Gharti Magars
Dagami, Galami, Kalikotey, Pahari or Panre, Phagami, Rangu, Rawal, Rajali, Sawangi, Sene, Surai, Sinjapati, Sijapati, Talaji, Tirukia, Wale, Thini, Bhujel.

Pun Magars
Birkali, Baijali, Burduja, Paija, sain, Chochangi, Sinjali, Dut, Purja, Garbuja, Ramjali, Tilija, Armaja, Phungali, Sanangi, Sothi, Sutpahare, Khame, Khoroja, Thane, Tirke, Sabangi, Pahare, Gaura, Phagami/Fagami, Balali, Batha, Saureni, Sherpunja.

Rana Magars
Aachhami, Aslami, Bangling, Chumi, Gyangmi/Gyami, Kharka/Khadka, Kyapchaki/Kepchaki, Lungeli, Makkim, Maski, Marchu, Palli, Ruchal, Shrees, Surjabansi/Suryabangsi, Limel, Deuka, Jung, Fewali.

Roka Magars
Jelbangi, Dununge, Ramjali, Bajhangi, Baijali.

Thapa Magars
To name a few – Āthaghare, Bagale, Bakabal, Bakheti, Baraghare, Birkatta, Kala, Kammu, Khapangi, Palunge, Puwar/Punwar, Sunari, Sāthighare, Sinjali/Singjali, Saplangi, Midun, Mugmi, Pulami, Darlami, Salami, Jarga, Dhenga, Taramu, Tarami, Tarangi, Byangnasi, Masrangi

Gaha Thapa consists of Bucha, Gora, khangaha/khanga.

Reshmi Thapa consists of Dangal.

Saru Thapa consists of Jhapurluk, Jhendi/Jhedi, Kala. Besides these, Gurbachan, Purbachhaney, Phounja, Chauhan, Pachabhaiya, Khamcha, Khandaluk, Ghale, Baral, Somai, Pithakote, Jhakote, Rakaskoti/Raskoti, Uchai, Samal.

In former days, any Thapa who had lost three generations of ancestors in battle became a Rana, but with the prefix of his Thapa clan. Thus, a Reshmi Thapa would become a Reshmi Rana. An instance of this is to be found in the 5th Gurkhas, where a havildar, Lachman Thapa, and a naik, Shamsher Rana, descended from the two Thapa [Magars] brothers; but three generations of descendants from one of these brothers having been killed in the battle, Shamsher Rana's ancestors assumed the title of Rana while Lachman Thapa's ancestors not having been killed in battle for three generations remained a Thapa. From this custom many Rana sub clans are said to have sprung up, and this would lead one to believe that the Rana-Magar clan was looked up to amongst the Magars.

The Rana clan of Magar tribes come from the same stock of Thapa, but when they were separated from their original group and lost for three generations, they settled in a place called lamjung and called themselves by the name of Rana which means chief in khas tradition and language. Thus, the inhabitants of Rana Magar became the lamjung village. The Matwala Khas are generally the progeny of a Khas of Western Nepal and karnali with a Magar woman of Western Nepal. If the woman happens to belong to the khas mixed Rana clan of the Magar tribe, progeny is then called a Bhat Rana. The Matwala Khas doesn't wear the sacred thread. They eats pork and drinks alcohol, and in every way assimilates himself with the Magars. He invariably claims to be a matwali khas or pawai khas.

Linguistically, the Magars are divided into three groups. Baraha Magaratis speak Dhut dialect, whereas Athara Magaratis speak Pang and Kaike dialects.

Magar Dhut speakers: Rana, Ale, Thapa

Magar Kham speakers: Budhathoki, Pun, Roka, Gharti

Magar Kaike speakers: Tarali Magar of Dolpa; Budha, Gharti, Roka/Rokaya, Kayat, Jhakri all Magar clans residing in Dolpa and Karnali districts.

Language and script
Of the 1,887,733 Magar population in Nepal, about 788,530 speak Magar language as their mother tongue while the rest speak Nepali as their mother tongue. The western inhabitants of Nepal did not speak the language in the past. But recently, almost everyone has started learning the language. The Magar languages are rooted in the Bodic branch of the Tibetan family.

The Magar language, Magar Kura, is spoken in two major dialects and a number of sub dialects reflecting the geographic distribution of the group. The Western Magars of Rapti Zone speak Magar Kham language. In Dolpa District, Magars speak Magar Kaike language. Magar Dhut language speakers are all Magar clans residing in Twelve Magarat. Similarly Magar Kham language speakers are all Magar clans from Eighteen Magarat. Magar Kaike language speakers are all Magar clans in Karnali zone.

Magar Akkha or scripts are used in Sikkim as a Magar language script. Many scholars including MS Thapa have been in forefront to implement the Akkha script to write Magar language in Nepal. New generations have been learning it. Akkha script is said to be closely associated with Brahmi script.

Religion
As per Nepali census 79% of Magars follow Hinduism though there is high degree of syncretism with Buddhism, Animism and Ancestor Worship. Magars follow Buddhism and Hinduism. The original religions or beliefs of Magar people are Shamanism, Animism, Ancestor worship and northern Nepal's Magar follow Shamanism.

Magars are the main priests of the famous Manakamana Temple in Gorkha District, Budha Subba Temple in Dharan and Alamdevi temple (Nepal's former Shah Kings' mother Goddess or family deity) in Syangja District. In Manakamana Temple, specially, the priest must be a descendant of Saint Lakhan Thapa Magar, who is described as a spiritual guide for Ram Shah, and he had a very close relationship with the queen, who was considered an incarnation of the Goddess Durga Bhawani, an incarnation of Parvati. Similarly, Bhirkot, Gahraukot, Khilung, Nuwakot, Satahukot, Sarankot, Dhor, Lamjung, Gorkha Kalika, Salyankot Dhading also have Magar priests from Saru, Baral, Saru, Saru, Pulami, Chumi, Darlami, DudhrRana, Bhusal/Maski, Saru/Rana Magar clan respectively.

The main priests of Kalika, the goddess protecting the kingdoms of Lamjung and Gorkha, were also Bohara Magars. Magars have been in charge of the religious functions linked to the very source of Thakuri power.

Most Magars also follow a form of Tibetan Buddhism, with priests known as Lama Guru, forming the religious hierarchy. Buddhism is an important part of the culture even in the southern districts, where the Magars have developed a syncretic form of religion that combines earlier shamanistic and Buddhist rituals with Hindu traditions.

Animists and shamanism form part of the local belief system; their dhami (the faith healer or a kind of shaman) is called Dangar and their jhankri (another kind of faith healer or shaman) was the traditional spiritual and social leader of the Magars. Magars have an informal cultural institution, called Bhujel, who performs religious activities, organizes social and agriculture-related festivities, brings about reforms in traditions and customs, strengthens social and production system, manages resources, settles cases and disputes and systematizes activities for recreation and social solidarity.

Dress and ornaments
Men wear or wrap-on-loincloth, a bhangra, a bhoto or a shirt of vest, and the usual Nepali topi. Women wear the phariya or lunghi, chaubandhi cholo or a closed blouse and the heavy patuka or waistband, and the or shawl-like garment on the head.

The ornaments are the madwari on the ears, bulaki on the nose and the phuli on the left nostril, the silver coin necklace"[haari]" and the pote (yellow and Green beads) with the tilhari gold cylinder, [jantar], [dhungri], [naugedi], [phul], kuntha, and also raiya in the hand. Magar males do not wear many ornaments, but some are seen to have silver earrings, hanging from their earlobes, called "gokkul". The magar girls wear the amulet or locket necklace, and women of the lower hills and the high-altitude ones wear these made of silver with muga stones embedded in them and kantha. The bangles of silver and glass are also worn on their hands along with the sirbandhi, sirphuli and chandra on their heads. These are large pieces of gold beaten in elongated and circular shapes.

Festivals
Maghe Sankranti is considered to be one of the most important annual festivals of the indigenous Magar community. In fact, Maghe Sankranti is the government declared national festival of the Magar community as well as the Tharu community (2009 AD). It is celebrated on the first day of Magh (tenth month of the Nepali calendar, in mid-January), a time that marks the transition from winter to spring. According to the Magar terminology, Maghe Sakranti commemorates the end of udheli (literally 'down'), which is a period that lasts for six months starting from mid-July, and the initiation of ubheli ('up'), the period lasting for another six months starting from the mid-January. The down and up periods probably correspond to the annual cycle of herding livestock up and down from high pastures, a historically important economic activity of the Magars. The occasion is celebrated with a host of gatherings and special invitations to chelibetis, one's daughters and other female members of the family. Traditional Magar songs and dances are also performed. One of the most prominent food items prepared on this day (or any other celebratory occasion) is known as batuk (commonly known as 'bara'). It is considered to be a traditional food of the Magar people. Shaped like western doughnuts, it is made from black lentils that have been soaked for over twenty-four hours and are grounded to form a thick paste. It is then mixed with salt, pepper and turmeric and fried in oil. A perfect round shape is formed with the help of the palm, and a small distinct hole is made in the center.

Other major festivals of the Magar community are Bhume Puja, Chandi Purnima, Baisakhe Purnima, Mangsir Purnima, Jestha Purnima. Bhume Puja (worshipping the nature) is immensely celebrated in the Athara Magarat regions (Confederation of eighteen Magar Kingdoms), especially in Rukum, Rolpa and Pyuthan districts.

Magar people celebrates major festival like "Chhaigo" as Lhosar which is considered as the New Year for Magar community according to the Naagchi Sambat. Magar people also observe festivals like Chaiti, Rungma, Keja, Yacha etc. These festivals are based on the Tibetan Buddhism and the Bon culture.

Folk songs and dances
Magars have contributed phenomenally in Nepali folk songs and dances. Both men and women take part in folk songs and dances.

One of the most well-known Magar folk-dances is the Maruni dance during Tihar festival. In this dance, the main dancer wears a woman's dress, has someone to mimic her dance and one person to beat a Madal or Rani Madal. This dance is believed to be of divine origin and is directly linked with mythology. The role of the person beating the Madal is considered to be the most important, and even the one who mimics the main dancer is actually considered to be the protectors of the dancer. He wears a mask, entertains the crowd by his own gestures etc. The wearing of the dress by the dance is given a ritualistic position, as the dancer's dress, are elaborately laid along with flowers, rice etc. on a brass plate or a winnower. The dance begins with the worship of Madal, the dress, and other ornaments to be used by the dancer, followed by obeisance to all gods and goddesses like Saraswati, Ram, Sita. The dance ends with blessings to the family that has offered alms to the dancing group and brings the end to the dance ritualistically.

Another is Kauda, also known as Chudkha or Kanraha. Chudkha is a folk musical performance indigenous to the hilly regions of Nepal. Kauda was originated in the Magar community of Rising Ranipokhari, Tanahun. According to historians, it was originally called Kandraha dance. Although associated with its distinctive costume, musical instruments and prosody, some have expressed concern that Kaura is losing its authenticity due to perversions introduced by commercialization and external influence, while others have been more optimistic deeming the changes a natural part of the cultural evolution and increasing popularity.

The other major dances and songs originated from Magar community are Ghatu, Jhorra, Yanimaya, Sunimaya, Salaijo, Rung, Hurra , Bon Lama Nach and many more.

Occupations
Agriculture and the military are the primary sources of income. Magars constitute the largest number of Gurkha soldiers outside Nepal. Kaji Sarbajit Rana Magar became the head of government during the regency of Queen Rajendra Laxmi. Kaji Biraj Thapa Magar winner of limbuwan, Kaji Jayant Rana Magar was a Gorkhali general of the Gorkha Kingdom and the Kingdom of Kantipur, General Abhiman Singh Rana Magar and Kaji Sarbajit Rana Magar headed the Nepal army. Biraj Thapa Magar was the first army chief in Nepal Army's history.

Dor Bahadur Bista's observation of Magar's occupation during the 1960s was: "Some of the northernmost Magars have become quite prosperous by engaging in long-range trading that takes them from near the northern border to the Terai, and even beyond to Darjeeling and Calcutta. Were it not for their role in the Gurkha regiments of the Indian and British armies, their self-sufficiency might be endangered."

Toni Hagen, who did his field research in Nepal during the 1950s, observed: "Magars possess considerable skill as craftsmen: they are the bridge builders and blacksmiths among the Nepalese, and the primitive mining is largely in their hands. On the lower courses of the Bheri & Karnali rivers, a great number of Magars annually migrate to the Terai & there manufacture bamboo panniers, baskets, and mats for sale in the bazaars along the borders. In their most northerly settlement, on the other hand, the important trading centre of Tarakot on the Barbung river, they have largely adopted their way of life, their clothes, and their religion to that of the Tibetans; like the latter, they also live by the salt trade. As regard race, the Magars have almond-shaped eyes or even open eyes, whereas Mongoloid eyes are very rare."

Military service
A number of Magars have distinguished themselves in military service under Nepali, British and Indian military. During Anglo-Nepalese War (1814–16), the Magar Unit/Paltan of Nepali Army, Purano Gorakh Battalion, valiantly fought the Battle of Nalapani. Brigadier General Sher Jung Thapa received Mahavir Chakra and Lieutenant Colonel Dhan Singh Thapa won Paramvir Chakra, the highest gallantry award, while serving Indian Army. Similarly, Dipprasad Pun, a Nepalese Sergeant of the Royal Gurkha Rifles (British Army), was the first Nepali winner of the Conspicuous Gallantry Cross in Afghanistan in 2010. In the two world wars, a total of 5 Victoria Cross (out of 13 VCs awarded to Gurkhas) were awarded to the Magars:
 * First World War:
 * VC Rifleman Kulbir Thapa was the first Gurkha to win Victoria Cross in recognition of his valor and bravery. He was from Gulmi, Bharse. He served in 2/3 Gurkha Regiment (GR). He received Victoria Cross in France in 1915.
 * VC Rifleman Karanbahadur Rana, Gulmi was from 2/3 GR. He was awarded the Victoria Cross for valour on 10 Apr 1917 at El Kafr in Palestine.
 * Second World War:
 * VC Subedar Lalbahadur Thapa, Nepal Tara was from 2nd GR. He received Victoria Cross in Tunisia in 1943.
 * VC Honorary Lieutenant Tul Bahadur Pun was from 6th GR. He received Victoria Cross in Burma in 1944.
 * VC Subedar Netrabahadur Thapa was from 5th GR. He received Victoria Cross in Burma in 1944.

Politics

Magars since the formation of Nepali state had been in a very influential role in the Nepali government until the Kot Massacre. During the time of King Prithvi Narayan Shah and thereafter, Magars were one of the six courtiers of Kings. Nepali military historian Brigadier General (retired) Dr Prem Singh Basnyat also confirm the high government positions held by the Magars notably Biraj Thapa Magar, Kaji Jayant Rana Magar, Kaji Bandhu Rana, Kaji Sarbajit Rana Magar and Abhiman Singh Rana Magar. During the Rana Dynasty, Magars almost had nil representation in any government positions, which can be considered the darkest time.

Under the leadership of minister Giri Prasad Burathoki, a first ever Magar Convention was held in Bharse of Gulmi District, one of the 12 Magarats in 1957. The objective of the conference was to sensitize the Magars to come forward in the national spectrum. Later Magar political and social organisations included Nepal Langhali Pariwar (1972), Nepal Langhali Pariwar Sang, and Langhali Pariwar Sangh.

Nepal Magar Association is an un-biased and non-profit organization of Magar indigenous people. It is a common representative organization of all the Magar indigenous people of Nepal and is committed to the preservation and promotion of Magar language and culture; the upliftment of the social-economic and the overall educational condition of the Magar people.

Notable Magars

 * Saint Lakhan Thapa (17th century), a spiritually famed associate and adviser to King Ram Shah and the first Priest of Manakamana Temple.
 * Kaji Biraj Thapa Magar of Gorkha, the 'King Maker'. From the list of people with title Kaji.
 * Kaji Biraj Thapa Magar, the first Chief of Gorkhali Army, 18th century.
 * Kaji Jayant Rana Magar (Kaji of Gorkha and Kantipur) who commanded one battle for Gorkha and two battles for Kantipur against the invasion of Nuwakot.
 * Kaji Sarbajit Rana Magar, Nepalese Army Chief and prominent politician, 18th century.
 * Martyr Lakhan Thapa Magar (19th century), the first martyr of Nepal.
 * Kaji Abhiman Singh Rana Magar, Nepalese Army Chief, 19th century. He was the first victim of Kot massacre.
 * Master Mitrasen Thapa, famous Nepali folk singer, social worker, resident of Bhagsu/Dharmasala, (India).
 * Giri Prasad Burathoki, only Bada Hakim from Magars, Defense Minister, Honorary Major General of Nepalese Army.
 * Late Professor Jagat Bahadur Singh Burathokey, Father of Geography of Nepal.
 * Narayan Singh Pun, a former minister in Nepal, pilot and lieutenant colonel in the Royal Nepal Army. Also founding president of Nepal Samata Party.
 * Balaram Gharti Magar, held different ministries for 11 times including Defense Minister of Nepal Government.
 * Gore Bahadur Khapangi, former minister and founding leader of Prajatantrik Janamukti Party.
 * Rom Bahadur Thapa, First Inspector General of Nepal Police from Magar ethnic group.
 * Onsari Gharti Magar, the first female speaker of Parliament of Nepal.
 * Ram Bahadur Thapa Badal, Home minister of Nepal, leader Nepal Communist Party.
 * Barsaman Pun, First finance minister of Nepal from Magar community. He is from Rolpa district.
 * Nanda Bahadur Pun, First vice president of federal republic Nepal, former chief commander of the People's Liberation Army
 * Tham Maya Thapa, Women and Children Minister.
 * Ram Kumari Jhakri, a Nepalese politician, member of parliament and former president of All Nepal National Free Students Union (ANNFSU).
 * Kuber Singh Rana, Ex IGP Chief of Nepal Police from Palpa.
 * Mahabir Pun, Magsaysay Award winner for extending wireless technologies in rural parts of Nepal.
 * Dipprasad Pun, Conspicuous Gallantry Cross Winner During War in Afghanistan.
 * Tul Bahadur Pun, Honorary Lieutenant Victoria Cross Winner. Grandfather Of Dipprasad Pun.
 * Arun Thapa, popular Nepali singer.
 * Teriya Magar, Nepali dancer, winner of Dance India Dance Little Masters 2014
 * Nirmal Purja, famous mountaineer and Ex-British Gurkha soldier, (SBS) special forces Royal Navy, numerous Guinness World Records holder in mountaineering.
 * Laure (Nepalese rapper) Ashish Rana Magar, a Nepalese rapper, actor and Television personality popularly known by his stage name – "Laure".
 * Pramila Thapa, Taekwondo competitor in the 1992 Barcelona Olympics, black belt world champion and 10th degree black belt.
 * Prem Bahadur Ale,ex-minister of Forest and Environment. Minister of Culture,Tourism and Civil Aviation

title: Magars


text:
Holy Nail

Relics that are claimed to be the Holy Nails with which Jesus was crucified are objects of veneration among some Christians, particularly Roman Catholics and the Eastern Orthodox. In Christian symbolism and art, they figure among the Arma Christi or Instruments of the Passion, the objects associated with the Passion of Jesus. Like the other Instruments, the Holy Nails have become an object of veneration among many Christians and have been pictured in paintings.

The authenticity of these relics is doubtful. The Catholic Encyclopedia wrote: "Very little reliance can be placed upon the authenticity of the thirty or more holy nails which are still venerated, or which have been venerated until recent times, in such treasuries as that of Santa Croce in Rome, or those of Venice, Aachen, the Escurial, Nuremberg, Prague, etc. Probably the majority began by professing to be facsimiles which had touched or contained filings from some other nail whose claim was more ancient. Without conscious fraud on the part of anyone, it is very easy for imitations in this way to come in a very brief space of time to be reputed originals."

It is not clear whether Jesus was crucified with three or with four nails, and the question has been long debated. The belief that three nails were used is called Triclavianism.

The bridle and helmet of Constantine
Sozomen and Theodoret reported that when Helena, the mother of Constantine the Great, discovered the True Cross in Jerusalem in the fourth century AD, the Holy Nails were recovered too. Helena left all but a few fragments of the cross in the Church of the Holy Sepulchre in Jerusalem, but returned with the nails to Constantinople. As Theodoret tells it in his Ecclesiastical History, chapter xvii: "The mother of the emperor, on learning the accomplishment of her desire, gave orders that a portion of the nails should be inserted in the royal helmet, in order that the head of her son might be preserved from the darts of his enemies. The other portion of the nails she ordered to be formed into the bridle of his horse, not only to ensure the safety of the emperor, but also to fulfil an ancient prophecy; for long before Zechariah, the prophet, had predicted that 'There shall be upon the bridles of the horses Holiness unto the Lord Almighty."

The fifth-century Church historian of Constantinople, Socrates of Constantinople, wrote in his Ecclesiastical History, which was finished shortly after 439, that after Constantine was proclaimed Caesar and then Emperor, he ordered that all honor be paid to his mother Helena, to make up for the neglect paid her by her former husband, Constantius Chlorus. After her conversion to Christianity, Constantine sent her on a quest to find the cross and nails used to crucify Jesus. A Jew called Judas (in later retellings further called Judas Cyriacus) led her to the place where they were buried. Several miracles were claimed to prove the authenticity of these items, and Helena returned with a piece of the cross and the nails. Socrates wrote that one nail was used to make a bridle and one was used to make the Helmet of Constantine. Two relics exist that have the form of a bridle and are claimed to be the bridle of Constantine: one in the apse of the Cathedral of Milan, and the other in the cathedral treasury of Carpentras Cathedral.

The Iron Crown of Lombardy has been said to contain one of the nails; however, scientific analysis has shown that the crown contains no iron. The band that was supposed to have been formed from a nail is actually 99% silver.

Nails venerated as those of Jesus’s crucifixion

 * In the Basilica of Santa Croce in Gerusalemme in Rome (spike of a nail).
 * In the Holy Lance of the German imperial regalia in the Hofburg Palace in Vienna.
 * In the Iron Crown of Lombardy in the Cathedral of Monza.
 * In the treasury of Trier Cathedral.
 * In Bamberg Cathedral (middle part of a nail).
 * In the form of a bridle, in the apse of the Cathedral of Milan (see Rito della Nivola).
 * In the form of a bridle, in the cathedral treasury of Carpentras.
 * In the monastery of San Nicolò l'Arena in Catania (head of a nail).
 * In the cathedral of Colle di Val d'Elsa, near Siena.
 * In the Milevsko monastery in Czech Republic, discovered in 2020 in hidden vault.

title: Holy Nail