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Little Saint Hugh of Lincoln

Hugh of Lincoln (1246 – 27 August 1255) was an English boy whose death in Lincoln was falsely attributed to Jews. He is sometimes known as Little Saint Hugh or Little Sir Hugh to distinguish him from the adult saint, Hugh of Lincoln (died 1200). The boy Hugh was not formally canonised, so "Little Saint Hugh" is a misnomer.

Hugh became one of the best known of the blood libel "saints": generally Christian children whose deaths were interpreted as Jewish human sacrifices. It is believed by some historians that the church authorities of Lincoln steered events in order to establish a profitable flow of pilgrims to the shrine of a martyr and saint.

Hugh's death is significant because it was the first time that the Crown gave credence to ritual child murder allegations, through the direct intervention of King Henry III. It was further bolstered by Matthew Paris' account of the events, and by Edward I's support for the cult after his ordering of the expulsion of Jews from England, particularly his projection of power through the renovation of the tomb in the style of the Eleanor crosses.

As a result, in contrast to other English blood libels, the story entered the historical record, medieval literature and in ballads that circulated until the twentieth century.

Background
Allegations of ritual child murder had become increasingly common following the circulation of The Life and Miracles of St William of Norwich by Thomas of Monmouth, the hagiography of William of Norwich, a child-saint said to have been crucified by Jews in 1144. Other accusations followed, such as that of Harold of Gloucester (1168) and Robert of Bury (1181). The story of William and similar rumours influenced the myth that developed around Hugh. The accusations may have been promoted by church officials hoping to establish local cults to attract pilgrims and donations.

During the years running up to the accusation, King Henry III taxed English Jews heavily. This in turn forced Jewish moneylenders to ensure their debts were paid, with no flexibility, or to sell their debt bonds to Christians. The King's relatives and courtiers in particular would buy debt bonds, with the intention to seize the debtors' property as collateral. These policies of King Henry would later provoke the Second Barons' War.

Church restrictions against Jews also built up in the period. Pronouncements were made by the Vatican ordering that Jews live separate from Christians, that Christians were not to work for Jews, especially in their homes, and that Jews were to wear yellow badges to identify themselves. Church pronouncements in particular led to a number of English towns expelling their Jewish communities. Henry III codified most of the Church's demands and put them into enforceable law in his 1253 Statute of Jewry.

At the time of the Hugh of Lincoln murder accusations, Henry III had sold his rights to tax English Jews to his brother, Richard, Earl of Cornwall. The King decreed that if any Jew were convicted of a crime, his money and property would then be forfeit to the Crown.

A number of Jews from across England had gathered in Lincoln to attend a wedding at the time of the child's death.

The accusation and myth
The nine-year-old Hugh disappeared on 31 July, and his body was discovered in a well on 29 August. It was claimed that Jews had imprisoned Hugh, during which time they tortured and eventually crucified him. It was said that the body had been thrown into the well after attempts to bury it failed, when the earth had expelled it.

The chronicler Matthew Paris described the supposed murder, implicating all the Jews in England:

This year [1255] about the feast of the apostles Peter and Paul [27 July], the Jews of Lincoln stole a boy called Hugh, who was about eight years old. After shutting him up in a secret chamber, where they fed him on milk and other childish food, they sent to almost all the cities of England in which there were Jews, and summoned some of their sect from each city to be present at a sacrifice to take place at Lincoln, in contumely and insult of Jesus Christ. For, as they said, they had a boy concealed for the purpose of being crucified; so a great number of them assembled at Lincoln, and then they appointed a Jew of Lincoln judge, to take the place of Pilate, by whose sentence, and with the concurrence of all, the boy was subjected to various tortures. They scourged him till the blood flowed, they crowned him with thorns, mocked him, and spat upon him; each of them also pierced him with a knife, and they made him drink gall, and scoffed at him with blasphemous insults, and kept gnashing their teeth and calling him Jesus, the false prophet. And after tormenting him in diverse ways they crucified him, and pierced him to the heart with a spear. When the boy was dead, they took the body down from the cross, and for some reason disembowelled it; it is said for the purpose of their magic arts.

While the Paris account is significant as the most famous and influential version of the myth, due to his own popularity as a chronicler and talent as storyteller, it is also thought to be the least reliable, and most fabricated, of the contemporary accounts of what had supposedly taken place. Other contemporary accounts include the Annals of Waverley and of Burton Abbey.

Role of the Bishop
A Jew, Copin, reportedly confessed to the murder. He was also offered immunity from sentencing in return for his confession according to contemporary accounts. Copin appears to have been interrogated under torture by John of Lexington, brother of Henry, the new Bishop of Lincoln, and servant of the King. This leads to the conclusion by modern historians that there was likely clerical collusion to give credence to the accusation, with the aim of profiting from a new cult with pilgrims and their gifts.

Royal intervention
A number of events exacerbated the impact of this event. Henry III arrived in Lincoln around a month after the initial arrest and confession. He ordered Copin to be executed, and for ninety Jews to be arrested at random in connection with Hugh's disappearance and death and held in the Tower of London. They were charged with ritual murder. Eighteen of the Jews were hanged for refusing to participate in the proceedings, claiming this was a show trial and refusing to throw themselves on the mercy of a Christian jury. Gavin I. Langmuir says:

"What distinguished the Lincoln affair from other accusations of ritual murder was that the king took personal cognizance and had one Jew executed immediately and eighteen others spectacularly executed later. That royal substantiation of the truth of the charge was probably decisive for Hugh's fame, which far outshadowed that of William of Norwich, Harold of Gloucester, Robert of Bury St. Edmunds, and the poor anonymous infant of St. Paul's."

Garcias Martini, knight of Toledo, interceded for the release of Benedict son of Moses of London, probably the father of Belaset, whose wedding had been taking place. In January a further pardon was extended to a Christian Jew, John after the intervention of a Dominican friar. A trial took place on 3 February at Westminster for the remaining 71 prisoners. They were condemned to death by a jury of 48. After this point either the Dominicans or Franciscans interceded, together with Richard of Cornwall. By May, the prisoners were released. It may be that doubt as to their guilt had set in, as it is unlikely that the monks or Richard would have interceded without thinking the charge was false, given the severity of the charge.

The difficulty remains as to why King Henry and his servant John of Lexington would have believed the accusations in the first place. For Lexington, his motivations may be his personal connections to the clerics of Lincoln, including his brother the Bishop, who stood to benefit from the veneration of the 'martyr' Hugh. He may have believed, or wished to believe, what he heard. While the decision to act belonged to the King, Langmuir believes that he was weak and easily manipulated by Lexington. Langmuir says Henry III has been described as; "a suspicious person who flung charges of treason recklessly, [who] was credulous and poor in judgment, and often appeared like a petulant child. When to these qualities we add his addiction to touring the shrines of England, it becomes easier to understand why he acted as he did, both when he heard Copin's confession and when the friars and cooler heads intervened later." Langmuir therefore concludes that Lexington "incited the weakly credulous Henry III to give the ritual murder fantasy the blessing of royal authority". Jacobs on the other hand sees the financial benefits that Henry received as a major factor, conscious or unconscious, in his decision to arrest en masse and execute Jews. As noted above, he had mortgaged his income from the Jews to Richard of Cornwall, but was still entitled to the property of any Jew executed, adding that Henry, "like most weak princes, was cruel to the Jews".

Veneration
After news spread of his death, miracles were attributed to Hugh; and he became one of the youngest individual candidates for sainthood, with 27 July unofficially made his feast day. Many local 'saints' of the medieval period were not canonised but were locally dubbed saints and venerated. 'Little Saint Hugh' was for a while acclaimed as a saint by local people but never officially recognised as one. Over time, the issue of the rush to sainthood was raised, and Hugh was never canonised and was never a part of the official Catholic calendar of saints. The Vatican never included the child Hugh in Catholic martyrology and his traditional English feast day is not celebrated.

Lincoln Cathedral benefited from the episode; Hugh was regarded as a Christian martyr, and sites associated with his life became objects of pilgrimage.

The shrine dated to the period immediately after the expulsion of the Jews from England in 1290, partly funded by Edward I, as a propaganda tool helping to justify his actions by emphasising the danger that Jews supposedly posed to Christians. The royal coat of arms was prominently displayed. As Stacey notes: "A more explicit identification of the crown with the ritual crucifixion charge can hardly be imagined." The design included decoration commemorating Edward I's wife Eleanor of Castile, who had been widely disliked for large-scale buying and selling of Jewish bonds, with the aim of requisitioning the lands and properties of those indebted; it may have deliberately echoed that of the Eleanor crosses, also commemorating her. This intervention was a major "propaganda coup" rehabilitating Edward and Eleanor's image and claiming credit for the Expulsion.

While popular into the 1360s, the cult seems to have declined in the next half century, as it was raising just 10½d. in 1420–21. The shrine was largely destroyed after the English Reformation. During the Cathedral restoration of 1790 a stone coffin, 3 feet 3 inches (1 metre) long, was found containing the skeleton of a boy; this was drawn by Samuel Hieronymus Grimm.

Legacy and significance
The myth of ritual child murder was a continuing theme in anti-semitism and long-standing in English culture. The Hugh story is referenced by Geoffrey Chaucer's Canterbury Tales in The Prioress's Tale. Christopher Marlowe also apparently refers to the story in The Jew of Malta, where Friar Jacomo at the end of Act Three asks of a Jew, "What, has he crucified a child?" Again, Marlowe may have known the story through Paris's account. The story is retold as fact in Thomas Fuller's 1662 Worthies of England.

Ballads referring to the incident circulated in England, Scotland and France. The earliest English and French versions appear to have been composed near the time. The "Sir Hugh" ballad went through many variations, and was still well known into the nineteenth and twentieth century, when versions could be found in the United States.

Langmuir describes the fantasy concocted by Lexington as contributing to some of the darkest strands of anti-Jewish prejudice. Lexington:

"inspired Matthew Paris to write a vivid garbled yarn that would ring in men's minds for centuries and blind modern historians. A century and a half later, Geoffrey Chaucer, after letting the legend of the singing boy slip from the prioress's lips, would inevitably be reminded of England's most famous proof of Jewish evil and conclude with an invocation to young Hugh – whose alleged fate neither he nor his audience were likely to question. John de Lexinton died in January, 1257, and his elegant learning will not be described in any history of mediaeval thought, yet his tale of young Hugh of Lincoln became a strand in English literature and a support for irrational beliefs about Jews from 1255 to Auschwitz. It is time he received his due 'credit' for such wickedness."

The Hugh myth continued to resonate into the nineteenth century, when European antisemitic polemicists attempted to 'prove' the veracity of the story. In the twentieth century, a well in the former Jewish neighbourhood of Jews' Court, Lincoln was advertised as 'the well in which Hugh's body was found', however this was found to have been constructed some time prior to 1928 to increase the tourist attraction of the property. A Lincolnshire preparatory school, St Hugh's School, Woodhall Spa, was named after Little St Hugh in 1925; its school badge featured a ball travelling over a wall.

In 1955, the Church of England placed a plaque at the site of Little Hugh's former shrine in Lincoln Cathedral, bearing these words:

By the remains of the shrine of "Little St Hugh".

Trumped up stories of "ritual murders" of Christian boys by Jewish communities were common throughout Europe during the Middle Ages and even much later. These fictions cost many innocent Jews their lives. Lincoln had its own legend and the alleged victim was buried in the Cathedral in the year 1255.

Such stories do not redound to the credit of Christendom, and so we pray:

Lord, forgive what we have been, amend what we are, and direct what we shall be.

History of the ballad

 * James Woodall, "'Sir Hugh': A Study in Balladry", Southern Folklore Quarterly, 19 (1955), 77— 84. https://hdl.handle.net/2027/mdp.39015038728997
 * Stamper, Frances C., and Wm. Hugh Jansen. ""Water Birch": An American Variant of "Hugh of Lincoln"." The Journal of American Folklore 71, no. 279 (1958): 16–22. doi:10.2307/537953.
 * See Chapter 11, The Survival of a Saint's Legend: Sir Hugh, or The Jew's Daughter (Child 155)
 * See Chapter 11, The Survival of a Saint's Legend: Sir Hugh, or The Jew's Daughter (Child 155)

title: Little Saint Hugh of Lincoln


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Anusvara

Anusvara (अनुस्वार, ), also known as Bindu (बिंदु), is a symbol used in many Indic scripts to mark a type of nasal sound, typically transliterated or  in standards like ISO 15919 and IAST. Depending on its location in the word and the language for which it is used, its exact pronunciation can vary. In the context of ancient Sanskrit, anusvara is the name of the particular nasal sound itself, regardless of written representation.

Sanskrit
In Vedic Sanskrit, the anusvāra (lit. "after-sound" or "subordinate sound") was an allophonic (derived) nasal sound.

The exact nature of the sound has been subject to debate. The material in the various ancient phonetic treatises points towards different phonetic interpretations, and these discrepancies have historically been attributed to either differences in the description of the same pronunciation or to dialectal or diachronic variation. In a 2013 reappraisal of the evidence, Cardona concludes that these reflect real dialectal differences.

The environments in which the anusvara could arise, however, were well defined. In the earliest Vedic Sanskrit, it was an allophone of /m/ at a morpheme boundary, or of /n/ within morphemes, when it was preceded by a vowel and followed by a fricative. In later Sanskrit its use expanded to other contexts, first before /r/ under certain conditions, then, in Classical Sanskrit, before and.

Later still, gave anusvara as an alternative pronunciation as word-final sandhi, and later treatises also prescribed it at morpheme junctions and within morphemes. In the later written language, the diacritic used to represent anusvara was optionally used to indicate a nasal stop having the same place of articulation as a following plosive, written in some evolved scripts (e.g. in Bengali-Assamese) as an additional sandhi letter (no longer as a diacritic) for Vedic transcriptions of Sanskrit, to distinguish it with the anusvara diacritic used to transcribe other phonemes.

Devanagari script
In the Devanagari script, anusvara is represented with a dot (bindu) above the letter (e.g. मं ). In the International Alphabet of Sanskrit Transliteration (IAST), the corresponding symbol is ṃ (m with an underdot). Some transcriptions render notation of phonetic variants used in some Vedic shakhas with variant transcription (ṁ).

In writing Sanskrit, the anusvara is often used as an alternative representation of the nasal stop with the same place of articulation as the following plosive. For example, 'limb (of the body)' may be written with either a conjunct, अङ्ग aṅga, or with an anusvara, अंग aṃga. A variant of the anusvara, the anunāsika or 'chandrabindu', was used more explicitly for nasalized vowels, as in अँश aṃśa for 'portion'.

Hindi
In Standard Hindi, the  is traditionally defined as representing a nasal consonant homorganic to a following plosive, in contrast to the candrabindu (anunāsika), which indicates vowel nasalization. In practice, however, the two are often used interchangeably.

The precise phonetic value of the phoneme, whether it is represented by anusvāra or candrabindu, is dependent on the phonological environment.

Word-finally it is realized as nasalization of the preceding vowel: kuāṃ, "a well". It results in vowel nasalization also medially between a short vowel and a non-obstruent (kuṃvar "a youth", gaṃṛāsā  "a long-handled axe") and, in native words, between a long vowel and a voiceless plosive (dāṃt  "tooth", sāṃp  "a snake", pūṃch  "tail").

It is pronounced as a homorganic nasal, with the preceding vowel becoming nasalized allophonically, in the following cases: between a long vowel and a voiced plosive (tāṃbā "copper", cāṃdī  "silver"), between a long vowel and a voiceless plosive in loanwords (dāṃt  "repressed", baiṃk  "a bank", khazāṃcī  "cashier"), and between a short vowel and an obstruent (saṃbhāl-  "to support", saṃdūk  "a chest").

The last rule has two sets of exceptions where the anusvāra only results in nasalization of the preceding short vowel. Words from the first set are morphologically derived from words with a long nasalized vowel (baṃṭ-, "to be divided"  from bāṃṭ- , "to divide";  siṃcāī , "irrigation" from sīṃc- , "to irrigate"). In such cases, the vowel is sometimes denasalized (, instead of, ). The second set is composed of a few words like (pahuṃc-, "to arrive" and haṃs- , "to laugh").

Marathi
In Marathi the anusvara is pronounced as a nasal that is homorganic to the following consonant (with the same place of articulation). For example, it is pronounced as the dental nasal न् before dental consonants, as the bilabial nasal म् before bilabial consonants, etc . Unlike in other Indic languages, in Marathi the same dot designating anusvara is also used to mark a retension of the inherent vowel (it is inconsistently placed over a consonant after which the short central vowel is to be pronounced and not elided).

Nepali
In Nepali, candrabindu indicates vowel nasalization. Therefore, there is a great deal of variation regarding which occurs in any given position. Many words containing anusvara thus have alternative spellings with chandrabindu instead of anusvara and vice versa. Anusvara is used when there isn't space for chandrabindu.Anusvara can represent nasal vowel, homoorganic nasal or somethimes both.

Other Indic script languages
Anusvara is used in other languages using Indic scripts as well, usually to represent suprasegmental phones (such as phonation type or nasalization) or other nasal sounds.

Bengali
In the Bengali script, the anusvara diacritic (অনুস্বার) is written as a circle above a slanted line ( ং ), and represents /ঙ্/. It is used in the name of the Bengali language বাংলা. It has merged in pronunciation with the letter ঙ unga in Bengali. Although the anusvara is a consonant in Bengali phonology, it is nevertheless treated in the written system as a diacritic in that it is always directly adjacent to the preceding consonant, even when consonants are spaced apart in titles or banners: বাং-লা-দে-শ baṅ-la-de-ś, not বা-ং-লা-দে-শ ba-ṅ-la-de-ś for বাংলাদেশ Bangladesh. It is never pronounced with the inherent vowel 'ô', and it cannot take a vowel sign (instead, the consonant ঙ uṅô is used pre-vocalically).

Burmese
In the Burmese script, the anusvara (MY အောက်မြစ် auk myit (့) ) is represented as a dot underneath a nasalised final to indicate a creaky tone (with a shortened vowel). Burmese also uses a dot above to indicate the nasalized ending (called "Myanmar Sign Anusvara" in Unicode), called MY သေးသေးတင် thay thay tin  (ံ)

Sinhala
In the Sinhala script, the anusvara is not a nonspacing combining mark but a spacing combining mark. It has circular shape and follows its base letter ( ං). It is called in Sinhala, which means "dot". The anusvara represents at the end of a syllable. It is used in fact, in the name of the Sinhala language සිංහල. It has merged in pronunciation with the letter ඞ ṅa in Sinhala.

Telugu
The Telugu script has full-zero (sunna) ం, half-zero (arasunna) and visarga to convey various shades of nasal sounds. Anusvara is represented as a circle shape after a letter: క - ka and కం - kam.

Thai
The equivalent of the anusvara in the Thai alphabet is the nikkhahit (◌ํ), which is used when rendering Sanskrit and Pali texts. It is written as an open circle above the consonant (for example อํ) and its pronunciation depends on the following sound: if it is a consonant then the nikkhahit is pronounced as a homorganic nasal, and if it is at the end of a word it is pronounced as the Voiced velar nasal.

Anunasika
Anunasika () is a form of vowel nasalization, often represented by an anusvara. It is a form of open-mouthed nasalization, akin to the nasalization of vowels followed by "n" or "m" in Parisian French. When "n" or "m" follow a vowel, the "n" or "m" becomes silent and causes the preceding vowel to become nasal (pronounced with the soft palate extended downward so as to allow part or all of the air to leave through the nostrils). Anunasika is sometimes called a subdot because of its IAST representation.

In Devanagari and related orthographies, it is represented by the chandrabindu diacritic (example: माँ).

In Burmese, the anunasika, called MY သေးသေးတင် and represented as $⟨ံ⟩$, creates the  nasalized ending when it is attached as a dot above a letter. The anunasika represents the -m final in Pali.

Unicode
Unicode encodes anusvara and anusvara-like characters for a variety of scripts:

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

title: Anusvara


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Talk:Stephen Schneider (scientist)

Appearance on In Search Of.
Stephen Schneider appeared on an episode of "In Search Of" where he discussed the next ice age. —Preceding unsigned comment added by 65.122.202.130 (talk) 22:41, 20 April 2010 (UTC)

Restore: why
I've restored some of the early stuff. It is constantly being referred to, so having a correct version available is good William M. Connolley (talk) 12:01, 13 June 2010 (UTC)

Former denialist
Shouldn't Schneider's notorious past as a global warming denialist be mentioned in the lede? Kauffner (talk) 10:20, 8 July 2010 (UTC)

 * He doesn't sound like a denier in this 30 year old video Wikispan (talk) 11:08, 20 July 2010 (UTC)
 * People trying to frame Schneider as a former "denialist" do exist. They usually cite a 1971 paper, Rasool and Schneider, in which he and his co-auther contrasted the cooling effect of aerosols with the warming effect of carbon dioxide, based on what was known about both at the time.  He was a scientist, and changed his assessment as the scientific evidence accrued and clean fuel technology minimized the predicted aerosol problem.  See the discussion of the relevant paper in global cooling. --TS 14:52, 20 July 2010 (UTC)
 * So he wasn't somebody who denied the science at all. He was just trying to assemble a jigsaw, looking at the various pieces several different ways. As time moved forward, and more pieces slotted together, his position changed accordingly. All perfectly sensible. Wikispan (talk) 16:01, 20 July 2010 (UTC)
 * Also, what's a "denialist?" Is that something like a "round-earthist" or an "evolutionist?"  I can't keep up with all the new religious terms.  Is this like a "former heretic?"  —Preceding unsigned comment added by 68.61.156.96 (talk) 00:55, 10 September 2010 (UTC)
 * It's someone who denies that the increasing rate of CO2 production is a serious problem. --Vaughan Pratt (talk) 04:42, 29 October 2010 (UTC)

This "denialist" rubbish is just that, rubbish. Denialist should NOT be a term used, as it is an intended smear, and the fact that it's now used on Schneider shows how corrosive it is. The global temperature cooled from the end of World War 2 to the '70's, that is attested, and there were numerious "warnings" about how severe winters in North America etc were "signs" of an approaching, and unavoidable ice age! Possible warming WAS mooted (and had been since the time of Arrhenius), but the ice age was the coming catastrophy of the 1970's (apart from running out of oil). This is not some "lie" made up by the Heartland Institute as some ignoramouses with a political barrow to push love to assert, but was the "consensus" of the time. It was based upon empirical evidence, and upon the geological record of the glacial/interglacial cycle since the start of the Pleistocene - only some asserted it was down to aerosols and sulphates, others claimed it was the natural end of the interglacial. Pretending that there was no expectation of a cooling trend, possibly leading to the end of the interglacial - now that's REAL denialism! My issue with Schneider isn't that he once believed there was a cooling trend (there actually was), or that he speculated that this could be at least akin to the little ice age, but that when he changed to become one of the leading advocates for action against global warming at the end of the '80's he tried to downplay his earlier advocacy for global cooling. Changing ones mind on the basis of new data is what science is supposed to be about. Pretending you didn't, isn't. And can we stop the "denialism" smear? —Preceding unsigned comment added by 212.39.162.130 (talk) 15:19, 19 October 2010 (UTC)
 * Climate deniers found it convenient to recruit the late Roger Revelle to their cause by twisting what he said. They would appear to be pulling the same stunt with my fellow Stanford faculty member Stephen Schneider, who could not possibly have been more outspoken about the harm climate deniers were doing.  This could be compared to proponents of hate politics recruiting the late Jesus of Nazareth to their cause in the years following Jesus's crucifixion, had this sort of distortion been in vogue back then.  --Vaughan Pratt (talk) 04:29, 29 October 2010 (UTC)
 * Wikispan, you didn't go back far enough. You are correct that by 1980 Schneider was a global warming alarmist.  But in the early 1970s he was a global cooling alarmist.  The late John Daly (whose untimely death Phil Jones infamously called "cheering") documented many examples.
 * Vaughan et al, please be careful not to engage in insults or name-calling, like calling those who disagree with you "denialists" or "deniers" (a reference to Holocaust denial). It is forbidden by Wikipedia policy, and doing so in reply to 212.39.162.130's comment which points out that it's a smear makes doing so particularly egregious. NCdave (talk) 13:49, 15 April 2011 (UTC)
 * Ditto "alarmist" which is as much of a smear. RTFA, which explains how Schneider with Rasool in 1971 reported the evidence of their calculations suggesting cooling would predominate, then found a miscalculation and in 1974 published a retraction of his earlier findings. That's science, developing and refining analysis. John Lawrence Daly evidently objected to the science without himself being a scientist. Not a good source. . . dave souza, talk 19:44, 15 April 2011 (UTC)

Posthumous book
Schneider coauthored a book that will be published this fall by MIT Press. Should it be included on the page? http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=12333 76.119.237.37 (talk) 16:05, 21 July 2010 (UTC)
 * Added to the selected publications section. NW ( Talk ) 04:36, 23 July 2010 (UTC)

Obituary: Stephen Henry Schneider
http://www.nature.com/nature/journal/v466/n7309/full/466933a.html William M. Connolley (talk) 17:45, 24 August 2010 (UTC)
 * Add as external link? —Preceding unsigned comment added by 130.232.214.10 (talk) 09:50, 25 August 2010 (UTC)

http://dx.doi.org/10.1063/1.3541953 -Atmoz (talk) 00:49, 26 January 2011 (UTC)

Not a Nobel Prize Winner
The article says Schneider won the 2007 Nobel Peace Prize. That is not correct. That year's prize was shared by Al Gore and the Intergovernmental Panel on Climate Change (IPCC). See http://nobelprize.org/nobel_prizes/peace/laureates/2007/. Individual members of the IPCC are not Nobel laureates, just like individuals who served with UNICEF and the Red Cross. Each Nobel Prize can be awarded to no more than three winners per year, but the IPCC had perhaps hundreds of members and staff.

I will delay in removing this information for a few days to see if anyone offers a persuasive counterargument. — Preceding unsigned comment added by 71.160.106.224 (talk) 18:26, 5 August 2011 (UTC)

External links modified
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Reviewer Note
There are three people with this name. The actor is viewed almost ten times as often as the climate scientist/ Rather than change which is primary, I will be boldly making Stephen Schneider (disambiguation) primary. Robert McClenon (talk) 15:33, 10 July 2022 (UTC)

title: Talk:Stephen Schneider (scientist)


text:
Fermi gas

A Fermi gas is an idealized model, an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin. These statistics determine the energy distribution of fermions in a Fermi gas in thermal equilibrium, and is characterized by their number density, temperature, and the set of available energy states. The model is named after the Italian physicist Enrico Fermi.

This physical model is useful for certain systems with many fermions. Some key examples are the behaviour of charge carriers in a metal, nucleons in an atomic nucleus, neutrons in a neutron star, and electrons in a white dwarf.

Description
An ideal Fermi gas or free Fermi gas is a physical model assuming a collection of non-interacting fermions in a constant potential well. Fermions are elementary or composite particles with half-integer spin, thus follow Fermi–Dirac statistics. The equivalent model for integer spin particles is called the Bose gas (an ensemble of non-interacting bosons). At low enough particle number density and high temperature, both the Fermi gas and the Bose gas behave like a classical ideal gas.

By the Pauli exclusion principle, no quantum state can be occupied by more than one fermion with an identical set of quantum numbers. Thus a non-interacting Fermi gas, unlike a Bose gas, concentrates a small number of particles per energy. Thus a Fermi gas is prohibited from condensing into a Bose–Einstein condensate, although weakly-interacting Fermi gases might form a Cooper pair and condensate (also known as BCS-BEC crossover regime). The total energy of the Fermi gas at absolute zero is larger than the sum of the single-particle ground states because the Pauli principle implies a sort of interaction or pressure that keeps fermions separated and moving. For this reason, the pressure of a Fermi gas is non-zero even at zero temperature, in contrast to that of a classical ideal gas. For example, this so-called degeneracy pressure stabilizes a neutron star (a Fermi gas of neutrons) or a white dwarf star (a Fermi gas of electrons) against the inward pull of gravity, which would ostensibly collapse the star into a black hole. Only when a star is sufficiently massive to overcome the degeneracy pressure can it collapse into a singularity.

It is possible to define a Fermi temperature below which the gas can be considered degenerate (its pressure derives almost exclusively from the Pauli principle). This temperature depends on the mass of the fermions and the density of energy states.

The main assumption of the free electron model to describe the delocalized electrons in a metal can be derived from the Fermi gas. Since interactions are neglected due to screening effect, the problem of treating the equilibrium properties and dynamics of an ideal Fermi gas reduces to the study of the behaviour of single independent particles. In these systems the Fermi temperature is generally many thousands of kelvins, so in human applications the electron gas can be considered degenerate. The maximum energy of the fermions at zero temperature is called the Fermi energy. The Fermi energy surface in reciprocal space is known as the Fermi surface.

The nearly free electron model adapts the Fermi gas model to consider the crystal structure of metals and semiconductors, where electrons in a crystal lattice are substituted by Bloch electrons with a corresponding crystal momentum. As such, periodic systems are still relatively tractable and the model forms the starting point for more advanced theories that deal with interactions, e.g. using the perturbation theory.

1D uniform gas
The one-dimensional infinite square well of length L is a model for a one-dimensional box with the potential energy: $$V(x) = \begin{cases} 0, & x_c-\tfrac{L}{2} < x <x_c+\tfrac{L}{2},\\ \infty, & \text{otherwise.} \end{cases}$$

It is a standard model-system in quantum mechanics for which the solution for a single particle is well known. Since the potential inside the box is uniform, this model is referred to as 1D uniform gas, even though the actual number density profile of the gas can have nodes and anti-nodes when the total number of particles is small.

The levels are labelled by a single quantum number n and the energies are given by:

$$E_n = E_0 + \frac{\hbar^2 \pi^2}{2 m L^2} n^2. $$ where $$E_0$$ is the zero-point energy (which can be chosen arbitrarily as a form of gauge fixing), $$m$$ the mass of a single fermion, and $$\hbar$$ is the reduced Planck constant.

For N fermions with spin-1⁄2 in the box, no more than two particles can have the same energy, i.e., two particles can have the energy of $E_1$, two other particles can have energy $E_2$ and so forth. The two particles of the same energy have spin 1⁄2 (spin up) or −1⁄2 (spin down), leading to two states for each energy level. In the configuration for which the total energy is lowest (the ground state), all the energy levels up to n = N/2 are occupied and all the higher levels are empty.

Defining the reference for the Fermi energy to be $$E_0$$, the Fermi energy is therefore given by $$E_{\mathrm{F}}^{(\text{1D})}=E_{n}-E_0=\frac{\hbar^2 \pi^2}{2 m L^2} \left(\left\lfloor \frac{N}{2} \right\rfloor\right)^2,$$ where $\left\lfloor \frac{N}{2} \right\rfloor$ is the floor function evaluated at n = N/2.

Thermodynamic limit
In the thermodynamic limit, the total number of particles N are so large that the quantum number n may be treated as a continuous variable. In this case, the overall number density profile in the box is indeed uniform.

The number of quantum states in the range $$n_1 < n < n_1 + dn$$ is: $$D_n(n_1)\, dn = 2 \, dn\,.$$

Without loss of generality, the zero-point energy is chosen to be zero, with the following result:

$$E_n = \frac{\hbar^2 \pi^2}{2 m L^2} n^2 \implies dE = \frac{\hbar^2 \pi^2}{m L^2} n \, dn = \frac{\hbar \pi}{L}\sqrt{\frac{2E}{m}} dn \,.$$

Therefore, in the range: $$E_1=\frac{\hbar^2 \pi^2}{2 m L^2} n^2_1< E < E_1 + dE\,,$$ the number of quantum states is: $$D_n(n_1) \, dn = 2\frac{dE}{dE/dn} = \frac{2}{\frac{\hbar^2 \pi^2}{m L^2}n} \, dE \equiv D(E_1) \, dE\,.$$

Here, the degree of degeneracy is:

$$D(E)=\frac{2}{dE/dn} =\frac{2L}{\hbar \pi}\sqrt{\frac{m}{2E}} \,.$$

And the density of states is:

$$g(E)\equiv \frac{1}{L}D(E)=\frac{2}{\hbar \pi}\sqrt{\frac{m}{2E}}\,.$$

In modern literature, the above $$D(E)$$ is sometimes also called the "density of states". However, $$g(E)$$ differs from $$D(E)$$ by a factor of the system's volume (which is $$L$$ in this 1D case).

Based on the following formula:

$$\int^{E_\mathrm{F}}_{0} D(E) \, dE = N \,,$$

the Fermi energy in the thermodynamic limit can be calculated to be:

$$E_{\mathrm{F}}^{(\text{1D})}=\frac{\hbar^2 \pi^2}{2 m L^2} \left(\frac{N}{2}\right)^2\,.$$

3D uniform gas
The three-dimensional isotropic and non-relativistic uniform Fermi gas case is known as the Fermi sphere.

A three-dimensional infinite square well, (i.e. a cubical box that has a side length L) has the potential energy $$V(x,y,z) = \begin{cases} 0, & -\frac{L}{2}<x,y,z<\frac{L}{2},\\ \infty, & \text{otherwise.} \end{cases}$$

The states are now labelled by three quantum numbers nx, ny, and nz. The single particle energies are $$E_{n_x,n_y,n_z} = E_0 + \frac{\hbar^2 \pi^2}{2m L^2} \left( n_x^2 + n_y^2 + n_z^2\right) \,,$$ where nx, ny, nz are positive integers. In this case, multiple states have the same energy (known as degenerate energy levels), for example $$E_{211}=E_{121}=E_{112}$$.

Thermodynamic limit
When the box contains N non-interacting fermions of spin-$1⁄2$, it is interesting to calculate the energy in the thermodynamic limit, where N is so large that the quantum numbers nx, ny, nz can be treated as continuous variables.

With the vector $$\mathbf{n}=(n_x,n_y,n_z)$$, each quantum state corresponds to a point in 'n-space' with energy $$E_{\mathbf{n}} = E_0 + \frac{\hbar^2 \pi^2}{2m L^2} |\mathbf{n}|^2 \,$$

With $$ |\mathbf{n}|^2 $$denoting the square of the usual Euclidean length $$ |\mathbf{n}|=\sqrt{n_x^2+n_y^2+n_z^2} $$. The number of states with energy less than EF + E0 is equal to the number of states that lie within a sphere of radius $$|\mathbf{n}_{\mathrm{F}}|$$ in the region of n-space where nx, ny, nz are positive. In the ground state this number equals the number of fermions in the system:

$$N =2\times\frac{1}{8}\times\frac{4}{3} \pi n_{\mathrm{F}}^3 $$

The factor of two expresses the two spin states, and the factor of 1/8 expresses the fraction of the sphere that lies in the region where all n are positive. $$n_{\mathrm{F}}=\left(\frac{3 N}{\pi}\right)^{1/3} $$ The Fermi energy is given by $$E_{\mathrm{F}} = \frac{\hbar^2 \pi^2}{2m L^2} n_{\mathrm{F}}^2 = \frac{\hbar^2 \pi^2}{2m L^2} \left( \frac{3 N}{\pi} \right)^{2/3}$$

Which results in a relationship between the Fermi energy and the number of particles per volume (when L2 is replaced with V2/3):

This is also the energy of the highest-energy particle (the $$N$$th particle), above the zero point energy $$E_0$$. The $$N'$$th particle has an energy of $$ E_{N'} = E_0 + \frac{\hbar^2}{2m} \left( \frac{3 \pi^2 N'}{V} \right)^{2/3} \,=E_0 + E_{\mathrm{F}} \big |_{N'} $$

The total energy of a Fermi sphere of $$N$$ fermions (which occupy all $$N$$ energy states within the Fermi sphere) is given by:

$$E_{\rm T} = N E_0 + \int_0^N E_{\mathrm{F}}\big |_{N'} \, dN' = \left(\frac{3}{5} E_{\mathrm{F}} + E_0\right)N$$

Therefore, the average energy per particle is given by: $$ E_\mathrm{av} = E_0 + \frac{3}{5} E_{\mathrm{F}} $$

Density of states
For the 3D uniform Fermi gas, with fermions of spin-$1⁄2$, the number of particles as a function of the energy $N(E)$ is obtained by substituting the Fermi energy by a variable energy $(E-E_0)$ :

$$N(E)=\frac{V}{3\pi^2}\left[\frac{2m}{\hbar^2}(E-E_0)\right]^{3/2},$$

from which the density of states (number of energy states per energy per volume) $$g(E)$$ can be obtained. It can be calculated by differentiating the number of particles with respect to the energy:

$$g(E) =\frac{1}{V}\frac{\partial N(E)}{\partial E}= \frac {1}{2\pi^2} \left(\frac {2m}{\hbar^2}\right)^{3/2}\sqrt{E-E_0}.$$

This result provides an alternative way to calculate the total energy of a Fermi sphere of $$N$$ fermions (which occupy all $$N$$ energy states within the Fermi sphere):

$$\begin{align} E_T&=\int_0^N E \mathrm{d} N(E)=EN(E)\big |_0^N-\int_{E_0}^{E_0+E_F} N(E) \mathrm{d} E \\ &=(E_0+E_F)N-\int_{0}^{E_F} N(E) \mathrm{d} (E-E_0) \\ &=(E_0+E_F)N- \frac{2}{5}E_FN(E_F) = \left(E_0+\frac{3}{5} E_{\mathrm{F}}\right)N \end{align}$$

Degeneracy pressure
By using the first law of thermodynamics, this internal energy can be expressed as a pressure, that is $$P = -\frac{\partial E_{\rm T}}{\partial V} = \frac{2}{5}\frac{N}{V}E_{\mathrm{F}}= \frac{(3\pi^2)^{2/3}\hbar^2}{5m}\left(\frac{N}{V}\right)^{5/3},$$ where this expression remains valid for temperatures much smaller than the Fermi temperature. This pressure is known as the degeneracy pressure. In this sense, systems composed of fermions are also referred as degenerate matter.

Standard stars avoid collapse by balancing thermal pressure (plasma and radiation) against gravitational forces. At the end of the star lifetime, when thermal processes are weaker, some stars may become white dwarfs, which are only sustained against gravity by electron degeneracy pressure. Using the Fermi gas as a model, it is possible to calculate the Chandrasekhar limit, i.e. the maximum mass any star may acquire (without significant thermally generated pressure) before collapsing into a black hole or a neutron star. The latter, is a star mainly composed of neutrons, where the collapse is also avoided by neutron degeneracy pressure.

For the case of metals, the electron degeneracy pressure contributes to the compressibility or bulk modulus of the material.

Chemical potential
Assuming that the concentration of fermions does not change with temperature, then the total chemical potential μ (Fermi level) of the three-dimensional ideal Fermi gas is related to the zero temperature Fermi energy EF by a Sommerfeld expansion (assuming $$k_{\rm B}T \ll E_{\mathrm{F}}$$): $$\mu(T) = E_0 + E_{\mathrm{F}} \left[ 1- \frac{\pi ^2}{12} \left(\frac{k_{\rm B}T}{E_{\mathrm{F}}}\right) ^2 - \frac{\pi^4}{80} \left(\frac{k_{\rm B}T}{E_{\mathrm{F}}}\right)^4 + \cdots \right], $$ where T is the temperature.

Hence, the internal chemical potential, μ-E0, is approximately equal to the Fermi energy at temperatures that are much lower than the characteristic Fermi temperature TF. This characteristic temperature is on the order of 105 K for a metal, hence at room temperature (300 K), the Fermi energy and internal chemical potential are essentially equivalent.

Metals
Under the free electron model, the electrons in a metal can be considered to form a uniform Fermi gas. The number density $$N/V$$ of conduction electrons in metals ranges between approximately 1028 and 1029 electrons per m3, which is also the typical density of atoms in ordinary solid matter. This number density produces a Fermi energy of the order: $$E_{\mathrm{F}} = \frac{\hbar^2}{2m_e} \left( 3 \pi^2 \ 10^{28 \ \sim \ 29} \ \mathrm{m^{-3}} \right)^{2/3} \approx 2 \ \sim \ 10 \ \mathrm{eV}, $$ where me is the electron rest mass. This Fermi energy corresponds to a Fermi temperature of the order of 106 kelvins, much higher than the temperature of the Sun's surface. Any metal will boil before reaching this temperature under atmospheric pressure. Thus for any practical purpose, a metal can be considered as a Fermi gas at zero temperature as a first approximation (normal temperatures are small compared to TF).

White dwarfs
Stars known as white dwarfs have mass comparable to the Sun, but have about a hundredth of its radius. The high densities mean that the electrons are no longer bound to single nuclei and instead form a degenerate electron gas. The number density of electrons in a white dwarf is of the order of 1036 electrons/m3. This means their Fermi energy is:

$$E_{\mathrm{F}} = \frac{\hbar^2}{2m_e} \left( \frac{3 \pi^2 (10^{36})}{1 \ \mathrm{m^3}} \right)^{2/3} \approx 3 \times 10^5 \ \mathrm{eV} = 0.3 \ \mathrm{MeV}$$

Nucleus
Another typical example is that of the particles in a nucleus of an atom. The radius of the nucleus is roughly: $$R = \left(1.25 \times 10^{-15} \mathrm{m} \right) \times A^{1/3}$$ where A is the number of nucleons.

The number density of nucleons in a nucleus is therefore:

$$\rho = \frac{A}{ \frac{4}{3} \pi R^3} \approx 1.2 \times 10^{44} \ \mathrm{m^{-3}} $$

This density must be divided by two, because the Fermi energy only applies to fermions of the same type. The presence of neutrons does not affect the Fermi energy of the protons in the nucleus, and vice versa.

The Fermi energy of a nucleus is approximately: $$E_{\mathrm{F}} = \frac{\hbar^2}{2m_{\rm p}} \left( \frac{3 \pi^2 (6 \times 10^{43})}{1 \ \mathrm{m}^3} \right)^{2/3} \approx 3 \times 10^7 \ \mathrm{eV} = 30 \ \mathrm{MeV} ,$$ where mp is the proton mass.

The radius of the nucleus admits deviations around the value mentioned above, so a typical value for the Fermi energy is usually given as 38 MeV.

Density of states
Using a volume integral on $d$ dimensions, the density of states is:

$$g^{(d)}(E)=g_s \int\frac{\mathrm{d}^d\mathbf{k}}{(2\pi)^d}\delta\left(E-E_0-\frac{\hbar^2|\mathbf{k}|^2}{2m}\right)=g_s\ \left(\frac{m}{2\pi\hbar^2}\right)^{d/2} \frac{(E-E_0)^{d/2-1}}{\Gamma(d/2)} $$

The Fermi energy is obtained by looking for the number density of particles: $$\rho = \frac{N}{V} = \int_{E_0}^{E_0 + E_{\mathrm{F}}^{(d)}} g^{(d)}(E) \, dE$$

To get: $$E_{\mathrm{F}}^{(d)}=\frac{2\pi\hbar^2}{m}\left(\tfrac{1}{g_s}\Gamma\left(\tfrac{d}{2}+1\right)\frac{N}{V}\right)^{2/d}$$ where $V$ is the corresponding d-dimensional volume, $g_s$  is the dimension for the internal Hilbert space. For the case of spin-$1⁄2$, every energy is twice-degenerate, so in this case $g_{s}=2$.

A particular result is obtained for $$d=2$$, where the density of states becomes a constant (does not depend on the energy): $$g^{(2\mathrm{D})}(E) = \frac{g_s}{2}\frac{m}{\pi \hbar^2}. $$

Fermi gas in harmonic trap
The harmonic trap potential:

$$V(x,y,z) = \frac{1}{2}m\omega_x^2x^2+\frac{1}{2}m\omega_y^2y^2+\frac{1}{2}m\omega_z^2z^2$$

is a model system with many applications in modern physics. The density of states (or more accurately, the degree of degeneracy) for a given spin species is:

$$g(E) = \frac{E^2}{2(\hbar\omega_\text{ho})^3}\,,$$

where $$\omega_\text{ho}=\sqrt[3]{\omega_x\omega_y\omega_z}$$ is the harmonic oscillation frequency.

The Fermi energy for a given spin species is:

$$E_{\rm F}=(6N)^{1/3}\hbar\omega_\text{ho}\,.$$

Related Fermi quantities
Related to the Fermi energy, a few useful quantities also occur often in modern literature.

The Fermi temperature is defined as $T_{\mathrm{F}} = \frac{E_{\mathrm{F}}}{k_{\rm B}} $, where $$k_{\rm B}$$ is the Boltzmann constant. The Fermi temperature can be thought of as the temperature at which thermal effects are comparable to quantum effects associated with Fermi statistics. The Fermi temperature for a metal is a couple of orders of magnitude above room temperature. Other quantities defined in this context are Fermi momentum $ p_{\mathrm{F}} = \sqrt{2 m E_{\mathrm{F}}} $, and Fermi velocity $ v_{\mathrm{F}} = \frac{p_{\mathrm{F}}}{m}$ , which are the momentum and group velocity, respectively, of a fermion at the Fermi surface. The Fermi momentum can also be described as $$p_{\mathrm{F}} = \hbar k_{\mathrm{F}} $$, where $$k_{\mathrm{F}}$$ is the radius of the Fermi sphere and is called the Fermi wave vector.

Note that these quantities are not well-defined in cases where the Fermi surface is non-spherical.

Grand canonical ensemble
Most of the calculations above are exact at zero temperature, yet remain as good approximations for temperatures lower than the Fermi temperature. For other thermodynamics variables it is necessary to write a thermodynamic potential. For an ensemble of identical fermions, the best way to derive a potential is from the grand canonical ensemble with fixed temperature, volume and chemical potential μ. The reason is due to Pauli exclusion principle, as the occupation numbers of each quantum state are given by either 1 or 0 (either there is an electron occupying the state or not), so the (grand) partition function $$\mathcal{Z} $$ can be written as
 * $$\mathcal{Z}(T,V,\mu)=\sum_{\{q\}}e^{-\beta (E_q-\mu N_q)}=\prod_{q}\sum_{n_q=0}^1e^{-\beta(\varepsilon_q-\mu )n_q}=\prod_q\left(1+e^{-\beta(\varepsilon_q-\mu )}\right),$$

where $$\beta^{-1}=k_{\rm B}T $$, $$\{q\} $$ indexes the ensembles of all possible microstates that give the same total energy $E_q = \sum_{q} \varepsilon_q n_q $ and number of particles $N_q=\sum_{q} n_q $, $\varepsilon_q $  is the single particle energy of the state $q $  (it counts twice if the energy of the state is degenerate) and $n_q=0,1$ , its occupancy. Thus the grand potential is written as
 * $$\Omega(T,V,\mu)=-k_{\rm B}T\ln\left(\mathcal{Z}\right)=-k_{\rm B}T\sum_q\ln\left(1+e^{\beta(\mu-\varepsilon_q)}\right). $$

The same result can be obtained in the canonical and microcanonical ensemble, as the result of every ensemble must give the same value at thermodynamic limit $(N/V\rightarrow\infty) $. The grand canonical ensemble is recommended here as it avoids the use of combinatorics and factorials.

As explored in previous sections, in the macroscopic limit we may use a continuous approximation (Thomas–Fermi approximation) to convert this sum to an integral: $$\Omega(T,V,\mu) = -k_{\rm B} T \int_{-\infty}^\infty D(\varepsilon) \ln \left(1 + e^{\beta(\mu-\varepsilon)} \right) \, d\varepsilon $$ where $D(ε)$ is the total density of states.

Relation to Fermi–Dirac distribution
The grand potential is related to the number of particles at finite temperature in the following way $$N=-\left(\frac{\partial \Omega}{\partial \mu}\right)_{T,V}=\int_{-\infty}^\infty D(\varepsilon)\mathcal{f}\left(\frac{\varepsilon-\mu}{k_{\rm B}T}\right)\,\mathrm{d}\varepsilon $$ where the derivative is taken at fixed temperature and volume, and it appears $$\mathcal{f}(x)=\frac{1}{e^x+1} $$ also known as the Fermi–Dirac distribution.

Similarly, the total internal energy is $$U = \Omega - T\left(\frac{\partial \Omega}{\partial T}\right)_{V,\mu} - \mu\left(\frac{\partial \Omega}{\partial \mu}\right)_{T,V} = \int_{-\infty}^\infty D(\varepsilon) \mathcal{f} \!\left(\frac{\varepsilon-\mu}{k_{\rm B}T}\right) \varepsilon\, d\varepsilon. $$

Exact solution for power-law density-of-states
Many systems of interest have a total density of states with the power-law form: $$D(\varepsilon) = V g(\varepsilon) = \frac{V g_0}{\Gamma(\alpha)} (\varepsilon - \varepsilon_0)^{\alpha-1}, \qquad \varepsilon \geq \varepsilon_0$$ for some values of $g_{0}$, $α$, $ε_{0}$. The results of preceding sections generalize to $d$ dimensions, giving a power law with: For such a power-law density of states, the grand potential integral evaluates exactly to: $$\Omega(T,V,\mu) = - V g_0 (k_{\rm B}T)^{\alpha+1} F_{\alpha} \left( \frac{\mu - \varepsilon_0}{k_{\rm B}T} \right),$$ where $$F_{\alpha}(x)$$ is the complete Fermi–Dirac integral (related to the polylogarithm). From this grand potential and its derivatives, all thermodynamic quantities of interest can be recovered.
 * $α = d/2$ for non-relativistic particles in a $d$-dimensional box,
 * $α = d$ for non-relativistic particles in a $d$-dimensional harmonic potential well,
 * $α = d$ for hyper-relativistic particles in a $d$-dimensional box.

Relativistic Fermi gas
The article has only treated the case in which particles have a parabolic relation between energy and momentum, as is the case in non-relativistic mechanics. For particles with energies close to their respective rest mass, the equations of special relativity are applicable. Where single-particle energy is given by: $$E=\sqrt{(pc)^2 + (mc^2)^2}.$$

For this system, the Fermi energy is given by: $$E_{\mathrm{F}}=\sqrt{(p_{\mathrm{F}}c)^2+(mc^2)^2}-mc^2\approx p_{\mathrm{F}}c,$$ where the $$\approx$$ equality is only valid in the ultrarelativistic limit, and $$p_{\mathrm{F}} = \hbar\left(\frac{1}{g_s} 6\pi^2 \frac{N}{V}\right)^{1/3}.$$

The relativistic Fermi gas model is also used for the description of massive white dwarfs which are close to the Chandrasekhar limit. For the ultrarelativistic case, the degeneracy pressure is proportional to $$(N/V)^{4/3}$$.

Fermi liquid
In 1956, Lev Landau developed the Fermi liquid theory, where he treated the case of a Fermi liquid, i.e., a system with repulsive, not necessarily small, interactions between fermions. The theory shows that the thermodynamic properties of an ideal Fermi gas and a Fermi liquid do not differ that much. It can be shown that the Fermi liquid is equivalent to a Fermi gas composed of collective excitations or quasiparticles, each with a different effective mass and magnetic moment.

title: Fermi gas


text:
Red Allen

Henry James "Red" Allen, Jr. (January 7, 1908 – April 17, 1967) was an American jazz trumpeter and vocalist whose playing has been claimed by Joachim-Ernst Berendt and others as the first to fully incorporate the innovations of Louis Armstrong.

Life and career
Allen was born in the Algiers neighborhood of New Orleans, Louisiana, the son of the bandleader Henry Allen Sr. He took early trumpet lessons from Peter Bocage and Manuel Manetta.

Allen's career began in Sidney Desvigne's Southern Syncopators. He was playing professionally by 1924 with the Excelsior Brass Band and the jazz dance bands of Sam Morgan, George Lewis and John Casimir. After playing on riverboats on the Mississippi River, he went to Chicago in 1927 to join King Oliver's band. Around this time he made recordings on the side in the band of Clarence Williams.

After returning briefly to New Orleans, where he worked with the bands of Fate Marable and Fats Pichon, he was offered a recording contract with Victor Records and went to New York City, where he joined the Luis Russell band, which was later fronted by Louis Armstrong in the late 1930s.

In 1929, Allen joined Luis Russell's Orchestra, in which he was a featured soloist until 1932. He took part in recording sessions that year organized by Eddie Condon, some of which featured Fats Waller and Tommy Dorsey. He also made a series of recordings in late 1931 with Don Redman. In 1932 he recorded with the Rhythmakers in New York City. In 1933 he joined Fletcher Henderson's Orchestra, in which he stayed until 1934. He played with Lucky Millinder's Mills Blue Rhythm Band from 1934 to 1937, when he returned to Russell for three more years, by which time Russell's orchestra was fronted by Louis Armstrong. Allen seldom received any solo space on recordings with Armstrong, but was prominently featured in the band's live performances, even getting billing as a featured attraction.

As a bandleader, Allen recorded for Victor from 1929 through 1930. He made a series of recordings as co-leader with Coleman Hawkins in 1933 for ARC (Banner, Melotone, Oriole, Perfect, Romeo, etc.) and continued as an ARC recording artist through 1935, when he was moved to ARC's Vocalion label for a popular series of swing records from 1935 through late 1937. A number of these were popular at the time. He did a solitary session for Decca in 1940 and two sessions for OKeh in 1941. After World War II, he recorded for Brunswick in 1944, Victor in 1946, and Apollo in 1947.

Allen continued making many recordings under his own name and also with Fats Waller and Jelly Roll Morton and accompanied such vocalists as Victoria Spivey and Billie Holiday. After a short stint with Benny Goodman, Allen began to lead his own band at the Famous Door in Manhattan. He then toured with the band around the United States into the late 1950s.

In December 1957, Allen appeared with Pee Wee Russell on the television program Sound Of Jazz. In 1959, he made his first tour of Europe when he joined Kid Ory's band. He led the house band at New York's Metropole Cafe from 1954, until the club ceased its jazz policy in 1965.

Personal life and death
Allen was Catholic.

Allen returned to working under his own name and made numerous tours of the United States and Europe. He was diagnosed with pancreatic cancer in late 1966. After undergoing surgery, he made a final tour of England, which ended six weeks before his death, on April 17, 1967, in New York City. He is buried, in the newer section of Saint Raymond's Cemetery in the Bronx, in grave 52 of section 15. He was survived by his widow, Pearly May, and a son, Henry Allen III.

Style and influence
Allen's trumpet style has been described by Joachim-Ernst Berendt and others as the first to fully incorporate the innovations of Louis Armstrong, and to develop an emphasis on phrasing. Allen's recordings received much favorable attention. His versatility is shown by his winning of DownBeat awards in both the traditional jazz and the modern jazz categories.

In 2022, the New Orleans City Council voted to rename "Slidell Street" in Algiers to "Red Allen Way", in his honor.

Discography
With Langston Hughes
 * Red Allen, Kid Ory & Jack Teagarden at Newport (Verve, 1957)
 * Ride, Red, Ride in Hi-Fi (RCA Victor, 1957), later re released as World on a String (1991)
 * Mr. Allen (Swingville, 1962)
 * The College Concert with Pee Wee Russell (Impulse!, 1966)
 * Jazz Standards and Warhorses, with Coleman Hawkins (Jass Records, CD version 1987)
 * 1929–1933 (Chronological Classics 540, 1990)
 * Weary Blues (MGM, 1959)

title: Red Allen


text:
Eigil Nansen

Eigil Nansen (18 June 1931 – 27 February 2017) was the son of architect and humanist Odd Nansen and the grandson of explorer and humanist Fridtjof Nansen.

In 1991, he won The Lisl and Leo Eitinger Prize for his work with refugees and human rights. Nansen is also known for lighting the first Winter Olympic cauldron, in 1952.

title: Eigil Nansen


text:
Eldridge Cleaver

Leroy Eldridge Cleaver (August 31, 1935 – May 1, 1998) was an American writer and political activist who became an early leader of the Black Panther Party.

In 1968, Cleaver wrote Soul on Ice, a collection of essays that, at the time of its publication, was praised by The New York Times Book Review as "brilliant and revealing". Cleaver stated in Soul on Ice: "If a man like Malcolm X could change and repudiate racism, if I myself and other former Muslims can change, if young whites can change, then there is hope for America."

Cleaver went on to become a prominent member of the Black Panthers, having the titles Minister of Information and Head of the International Section of the Panthers, while a fugitive from the United States criminal justice system in Cuba and Algeria. Cleaver was convicted of a series of crimes including burglary, assault, rape, and attempted murder and eventually served time in Folsom and San Quentin prisons until being released on parole in 1968. In 1968 he became a fugitive after leading an ambush on Oakland police officers, during which two officers were wounded. Cleaver was wounded during the clash and Black Panther member Bobby Hutton was killed. As editor of the official Panthers' newspaper, The Black Panther, Cleaver's influence on the direction of the party was rivaled only by founders Huey P. Newton and Bobby Seale. Cleaver and Newton eventually fell out with each other, resulting in a split that weakened the party.

After spending seven years in exile in Cuba, Algeria, and France, Cleaver returned to the U.S. in 1975, where he became involved in various religious groups (Unification Church and CARP) before joining the Church of Jesus Christ of Latter-day Saints, as well as becoming a conservative Republican, appearing at Republican events.

Early life
Eldridge Cleaver was born in Wabbaseka, Arkansas. As a child he moved with his large family to Phoenix and then to Los Angeles. He was the son of Leroy Cleaver and Thelma Hattie Robinson. He had four siblings: Wilhelima Marie, Helen Grace, James Weldon, and Theophilus Henry. Both of his grandfathers were Protestant preachers.

As a teenager, he was involved in petty crime and spent time in youth detention centers. At the age of 18, he was convicted of a felony drug charge (marijuana) and sent to the adult prison at Soledad. In 1958, he was convicted of rape and assault with intent to murder, and served time in Folsom and San Quentin prisons. While in prison, he was given a copy of The Communist Manifesto.

Cleaver was released on parole December 12, 1966, with a discharge date of March 20, 1971. In 1968 he was arrested on violation of parole by association with individual(s) of bad reputation, and control and possession of firearms. Cleaver petitioned for habeas corpus to the Solano County Court, and was granted it along with a release of a $50,000 bail.

Black Panther Party
Cleaver was released from prison on December 12, 1966, with the help of Edward Michael Keating, founder of Ramparts magazine. He was writing for Ramparts magazine and organizing efforts to revitalize the Organization of Afro-American Unity. The Black Panther Party (BPP) was only two months old. He then joined the Oakland-based BPP, serving as Minister of Information, or spokesperson. What initially attracted Cleaver to the Panthers, as opposed to other prominent groups, was their commitment to armed struggle.

In 1967, Cleaver, along with Marvin X, Ed Bullins, and Ethna Wyatt, formed the Black House political/cultural center in San Francisco. Amiri Baraka, Sonia Sanchez, Askia Toure, Sarah Webster Fabio, Art Ensemble of Chicago, Avotcja, Reginald Lockett, Emory Douglas, Samuel Napier, Bobby Hutton, Huey Newton, and Bobby Seale were Black House regulars. The same year, he married Kathleen Neal Cleaver (divorced 1987), with whom he would have son Ahmad Maceo Eldridge (born 1969, Algeria; died 2018, Saudi Arabia) and daughter Joju Younghi (born July 31, 1970, North Korea).

Cleaver was a presidential candidate in 1968 on the ticket of the Peace and Freedom Party. Having been born on August 31, 1935, Cleaver would not have been the requisite 35 years of age until more than a year after Inauguration Day 1969. (Although the Constitution requires that the President be at least 35 years of age, it does not specify whether he need have reached that age at the time of nomination, or election, or inauguration.) Courts in both Hawaii and New York held that he could be excluded from the ballot because he could not possibly meet the Constitutional criteria.

In the aftermath of the assassination of Martin Luther King Jr. on April 4, 1968, there were riots across the nation. On April 6, Cleaver and 14 other Panthers were involved in a confrontation with Oakland police officers, during which two of the officers were wounded. Cleaver was wounded during the ambush and 17-year-old Black Panthers member Bobby Hutton was killed. They were armed with M16 rifles and shotguns. In 1980, he claimed that he had led the Panther group on a deliberate ambush of the police officers, thus provoking the shootout.

Some reporters were surprised by this move, because it was in the context of an uncharacteristic speech, in which Cleaver also discredited the Black Panthers, stated "we need police as heroes", and said that he denounced civilian review boards of police shootings for the "bizarre" reason that "it is a rubber stamp for murder". Some speculated Cleaver's admission could have been a pay-off to the Alameda County justice system, whose judge had only just days earlier let him escape prison time; Cleaver was sentenced to community service after getting charged with three counts of assault against three Oakland police officers. The PBS documentary A Huey Newton Story claims that "Bobby Hutton was shot more than twelve times after he had already surrendered and stripped down to his underwear to prove he was not armed." Charged with attempted murder after the incident, Cleaver jumped bail to flee to Cuba in late 1968. Initially treated with luxury by the Cuban government, the hospitality ended upon reports Fidel Castro had received information of the CIA infiltrating the Black Panther Party. Cleaver then decided to head to Algeria, sending word to his wife to meet him there. Elaine Klein normalized his status by getting him an invitation to attend the Pan-African Cultural festival, rendering him temporarily safe from prosecution.

The festival allowed him to network with revolutionaries from all over Africa in order to discuss the perils of white supremacy and colonialism. Cleaver was outspoken in his call to violence against the United States, contributing to his mission to "position the Panthers within the revolutionary nationalist camp inside the United States and as disciples of Fanon on the world stage". Cleaver had set up an international office for the Black Panthers in Algeria. Following Timothy Leary's Weather Underground-assisted prison escape, Leary stayed with Cleaver in Algiers; however, Cleaver placed Leary under "revolutionary arrest" as a counter-revolutionary for promoting drug use.

Cleaver cultivated an alliance with North Korea in 1969, and BPP publications began reprinting excerpts from Kim Il Sung's writings. Although leftists of the time often looked to Cuba, China, and North Vietnam for inspiration, few had paid any attention to the secretive Pyongyang regime. Bypassing U.S. travel restrictions on North Korea, Cleaver and other BPP members made two visits to North Korea in 1969–1970 with the idea that the juche model could be adapted to the revolutionary liberation of African-Americans. Taken on an official tour of the Democratic People's Republic of Korea, also known as North Korea, Cleaver expressed admiration at "the DPRK's stable, crime-free society which provided guaranteed food, employment, and housing for all, and which had no economic or social inequalities".

In the summer of 1970, Cleaver traveled to China as part a U.S. People's Anti-Imperialist Delegation along with another prominent party member, Elaine Brown.

Byron Vaughn Booth (former Panther Deputy Minister of Defense ) claimed that, after a trip to North Korea, Cleaver discovered that his wife had been having an affair with Clinton Robert Smith Jr., a fellow Black Panther. Booth told the FBI he had witnessed Cleaver shoot and kill Smith with an AK-47 in Algeria. Elaine Mokhtefi, in the London Review of Books, writes that Cleaver confessed the murder to her shortly after committing it.

In his 1978 book Soul on Fire, Cleaver made several claims regarding his exile in Algeria, including that he was supported by regular stipends from the government of North Vietnam, which the United States was then bombing. Cleaver stated that he was followed by other former criminals turned revolutionaries, many of whom (including Booth and Smith ) hijacked planes to get to Algeria.

Split and new directions
Eldridge Cleaver and Huey Newton eventually had a disagreement over the necessity of armed struggle as a response to COINTELPRO and other actions by the government against the Black Panthers and other radical groups, which led to Cleaver's eventual expulsion from the BPP. Also Cleaver's interest in North Korea and global anti-imperialist struggle drew ire from other BPP members who felt that he was neglecting the needs of African-Americans at home in the U.S. Following his expulsion from the Black Panthers in 1971, the group's ties with North Korea were quickly forgotten.

Cleaver advocated the escalation of armed resistance into urban guerrilla warfare, while Newton suggested the best way to respond was to put down the gun, which he felt alienated the Panthers from the rest of the black community, and focus on more pragmatic reformist activity by lobbying for increased social programs to aid African-American communities and anti-discrimination laws. Cleaver accused Newton of being an Uncle Tom for choosing to cooperate with white interests rather than overthrow them.

Cleaver left Algeria in 1972, moving to Paris, France, becoming a born again Christian during time in isolation living underground. He turned his hand to fashion design; three years later, he released codpiece-revival "virility pants" he called "the Cleavers", enthusing that they would give men "a chance to assert their masculinity". Cleaver returned to the United States in 1975 to face the unresolved attempted murder charge.

By September 1978, out on bail as the proceedings dragged on, he had incorporated Eldridge Cleaver Ltd, running a factory and West Hollywood shop exploiting his "Cleavers", which he claimed liberated men from "penis binding". He saw no conflict between this and his newfound Christianity, drawing support for his overtly sexual design from Deuteronomy 22. The long-outstanding charge was subsequently resolved on a plea bargain reducing it to assault. A sentence of 1,200 hours' community service was imposed.

Later life
In the early 1980s, Cleaver became disillusioned with what he saw as the commercial nature of evangelical Christianity and examined alternatives, including Sun Myung Moon's campus ministry organization CARP. He was also Catholic for a time. He later led a short-lived revivalist ministry called Eldridge Cleaver Crusades, "a hybrid synthesis of Islam and Christianity he called 'Christlam'", along with an auxiliary called the "Guardians of the Sperm".

Cleaver was then baptized into the Church of Jesus Christ of Latter-day Saints (LDS Church) on December 11, 1983. He periodically attended regular services and lectured by invitation at LDS gatherings.

By the 1980s, Cleaver had become a conservative Republican. He appeared at various Republican events and spoke at a California Republican State Central Committee meeting regarding his political transformation. In 1984, he ran for election to the Berkeley City Council but lost. Undaunted, he promoted his candidacy in the Republican Party primary for the 1986 Senate race but was again defeated. The next year, his 20-year marriage to Kathleen Neal Cleaver came to an end.

In 1988, Cleaver was placed on probation for burglary and was briefly jailed later in the year after testing positive for cocaine. He entered drug rehabilitation for a stated crack cocaine addiction two years later, but was arrested for possession by Oakland and Berkeley police in 1992 and 1994. Shortly after his final arrest, he moved to Southern California, falling into poor health.

Death
Cleaver died at age 62 on May 1, 1998, at Pomona Valley Hospital Medical Center in Pomona, California. He is buried at Mountain View Cemetery in Altadena, California.

Soul on Ice (1968)
"From my prison cell, I have watched America slowly coming awake. It is not fully awake yet, but there is soul in the air and everywhere I see beauty. I have watched the sit-ins, the freedom rides the Mississippi Blood Summers, demonstrations all over the country, the F.S.M. movement, the teach-ins, and the mounting protest over Lyndon Strangelove’s foreign policy —all of this, the thousands of little details, show me it is time to straighten up and fly right. That is why I decided to concentrate on my writings and efforts in this area. We are a very sick country —I, perhaps, am sicker than most. But I accept that. I told you in the beginning that I am extremist by nature —so it is only right that I should be extremely sick. I was very familiar with the Eldridge who came to prison, but that Eldridge no longer exists. And the one I am now is in some ways a stranger to me." While in prison, he wrote a number of philosophical and political essays, first published in Ramparts magazine and then in book form as Soul on Ice.

In the most controversial part of the book, Cleaver acknowledges committing acts of rape, stating that he initially raped black women in the ghetto "for practice" and then embarked on the serial rape of white women. He described these crimes as politically inspired, motivated by a genuine conviction that the rape of white women was "an insurrectionary act". When he began writing Soul on Ice, he unequivocally renounced rape and all his previous reasoning about it.

The essays in Soul on Ice are divided into four thematic sections: "Letters from Prison", describing Cleaver's experiences with and thoughts on crime and prisons; "Blood of the Beast", discussing race relations and promoting black liberation ideology; "Prelude to Love – Three Letters", love letters written to Cleaver's attorney, Beverly Axelrod; and "White Woman, Black Man", on gender relations, black masculinity, and sexuality.

title: Eldridge Cleaver


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Lee Remick

Lee Ann Remick (December 14, 1935July 2, 1991) was an American actress and singer. She was nominated for the Academy Award for Best Actress for the film Days of Wine and Roses (1962).

Remick made her film debut in A Face in the Crowd (1957). Her other notable film roles include Anatomy of a Murder (1959), Wild River (1960), Days of Wine and Roses (1962), No Way to Treat a Lady (1968), The Detective (1968), The Omen (1976), and The Europeans (1979).

She won Golden Globe Awards for the TV film The Blue Knight (1973), and for playing the title role in the miniseries Jennie: Lady Randolph Churchill (1974). For the latter role, she won the BAFTA TV Award for Best Actress. In April 1991, she received a star on the Hollywood Walk of Fame.

Remick also worked in theatre and in 1966 she was nominated for the Tony Award for Best Actress in a Play for her Broadway role in Wait Until Dark.

Early life
Remick was born in Quincy, Massachusetts, the daughter of Gertrude Margaret (two sources say Patricia ) (née Waldo), an actress, and Francis Edwin "Frank" Remick, who owned a department store. She had one older brother, Bruce. One of her maternal great-grandmothers, Eliza Duffield, was a preacher born in England.

Remick attended the Swoboda School of Dance and The Hewitt School.

Broadway and television
Remick made her Broadway theatre debut, age 18, in the 1953 production Be Your Age. She began guest starring on episodes of TV anthology series such as Armstrong Circle Theatre, Studio One in Hollywood, Robert Montgomery Presents, Kraft Theatre and Playhouse 90.

Early films
Remick made her film debut in Elia Kazan's A Face in the Crowd (1957). While filming the movie in Arkansas, Remick lived with a local family and practiced baton twirling so that she would be believable as the teenager who wins the attention of Lonesome Rhodes (played by Andy Griffith).

After appearing as Eula Varner, the hot-blooded daughter-in-law of Will Varner (Orson Welles) in The Long, Hot Summer (1958), she appeared in These Thousand Hills (1959) as a dance hall girl, both for 20th Century Fox.

Film stardom
Remick came to prominence portraying a rape victim whose husband is tried for killing her attacker in Otto Preminger's Anatomy of a Murder (1959).

She made a second film with Kazan, Wild River (1960), which co-starred Montgomery Clift and Jo Van Fleet. That year she played Miranda in a television version of The Tempest with Richard Burton. Remick was top-billed in Sanctuary (1961) alongside Yves Montand. She appeared in The Farmer's Daughter (1962) on television. She starred opposite Glenn Ford in the Blake Edwards suspense-thriller Experiment in Terror (1962). The same year, she was nominated for an Academy Award for Best Actress for her performance as the alcoholic wife of Jack Lemmon in Days of Wine and Roses (1962), also directed by Edwards. Bette Davis, also nominated that year for What Ever Happened to Baby Jane?, said "Miss Remick's performance astonished me, and I thought, if I lose the Oscar, it will be to her." They both lost to Anne Bancroft in The Miracle Worker.

When Marilyn Monroe was fired during the filming of the comedy Something's Got to Give, the studio announced that Remick would be her replacement. Co-star Dean Martin refused to continue, however, saying that while he admired Remick, he had signed onto the picture strictly to work with Monroe. Remick did The Running Man (1963) with Laurence Harvey and The Wheeler Dealers (1963), with James Garner.

Return to Broadway and 1965 films
Remick next appeared in the 1964 Broadway musical Anyone Can Whistle, with music and lyrics by Stephen Sondheim and a book and direction by Arthur Laurents, which ran for only one week. Remick's performance is captured on the original cast recording. This began a friendship between Remick and Sondheim, and she later appeared in the 1985 concert version of his musical Follies.

Remick returned to films with Baby the Rain Must Fall (1965), with Steve McQueen from a script by Horton Foote, and The Hallelujah Trail (1965) with Burt Lancaster.

In 1966, she starred in the Broadway play Wait Until Dark under the direction of Arthur Penn and co-starring Robert Duvall. It was a big success, and it ran for 373 performances; Remick was nominated for a Tony award for Best Actress (Dramatic). It was adapted into a successful film the following year starring Audrey Hepburn.

More films and 1970s
She performed in Damn Yankees! (1967) for TV and starred in No Way to Treat a Lady (1968) with Rod Steiger and George Segal, The Detective (1968) with Frank Sinatra, and Hard Contract (1969) with James Coburn.

Remick went to the UK to make Loot (1970) and A Severed Head (1971). Back in the U.S., she was in Sometimes a Great Notion (1971).

She appeared in Hennessy (1975), with Rod Steiger. She co-starred with Gregory Peck in the 1976 horror film The Omen. The film was a commercial success.

Remick followed it up with leading actress roles in Telefon (1977), with Charles Bronson; The Medusa Touch (1978) with Richard Burton; the television miniseries Wheels (1979) with Rock Hudson; Ike: The War Years (1979) portraying Kay Summersby; and The Europeans (1979) for director James Ivory.

Remick starred in many TV movies beginning with The Man Who Came to Dinner (1972) with Orson Welles. She followed it with Summer and Smoke (1972) for British TV; And No One Could Save Her (1973); Of Men and Women (1973), an unsuccessful pilot; The Blue Knight (1973) with William Holden; A Delicate Balance (1973) with Katharine Hepburn; QB VII (1974); Touch Me Not a.k.a. The Hunted (1974); Jennie: Lady Randolph Churchill (1975), playing the title role, which earned her an Emmy nomination; Hustling (1975) with Jill Clayburgh; A Girl Named Sooner (1975); Breaking Up (1978); and Torn Between Two Lovers (1979) with George Peppard.

1980s
Remick played Margaret Sullavan in Haywire (1980). She had the lead in The Women's Room (1980) and supporting roles in The Competition (1980) and Tribute (1980), the latter with Lemmon.

Remick starred in The Letter (1982), The Gift of Love: A Christmas Story (1983) and a TV adaptation of I Do! I Do! (1984). She had a role in the miniseries Mistral's Daughter (1984), adapted from the novel by Judith Krantz. The reviewer of The New York Times praised Remick for portraying Kate "to fresh-faced clawing perfection".

Remick was in Rearview Mirror (1984), Toughlove (1985), Of Pure Blood (1986), and Nutcracker: Money, Madness & Murder (1987). She went to Australia to make Emma's War (1987).

Remick's later performances include The Vision (1987) with Dirk Bogarde, Jesse (1988), Bridge to Silence (1989) and playing Sarah Bernhardt in Around the World in 80 Days (1989). Her last performance was the lead in the TV movie Dark Holiday (1989).

Recognition
Remick was awarded the Women in Film Crystal Award in 1990.

She has a star in the Motion Pictures section on the Hollywood Walk of Fame at 6104 Hollywood Boulevard. It was dedicated on April 29, 1991.

Personal life
Remick married producer Bill Colleran, whose credits include Your Hit Parade, The Dean Martin Show and The Judy Garland Show on August 3, 1957. They had two children, Katherine Lee Colleran (b. January 27, 1959) and Matthew Remick Colleran (b. June 7, 1961). Remick and Colleran divorced in 1968.

Remick married British producer William Rory "Kip" Gowans on December 18, 1970. He was an assistant director on films such as Darling (1965), Far from the Madding Crowd (1967) and The Lion in Winter (1968) before they married, and afterward worked on Sleuth (1972), The Man Who Fell to Earth (1976) and The Human Factor (1979). She moved with Gowans to England and remained married to him until her death. She starred in four telefilms he produced, The Women's Room (1980), The Letter (1982), Rearview Mirror (1984) and Of Pure Blood (1986). Remick and Gowans spent time in both England and Osterville, Massachusetts, which she considered her "true home".

Through her daughter, Remick had two grandchildren.

In the spring of 1989, Remick was diagnosed with kidney cancer. Treatments at first seemed to be successful. However, this proved not to be true, and she died on July 2, 1991, at the age of 55.

Popular culture
Remick was the subject of "Lee Remick", the 1978 debut single by the Australian indie rock band The Go-Betweens. Songwriter Robert Forster mistakenly thought Remick was from Ireland, and he makes references to this idea in the song. In reality, Remick was American-born and raised (as were her parents); after 1970, she divided her time between England (where she had family ancestry) and the U.S.

The British indie rock band Hefner recorded a song titled "Lee Remick" in 1998, unrelated to the Go-Betweens' single.

title: Lee Remick