Patricia Godi

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Hilary Holladay

Power and Change in Adrienne Rich's Poetry, or Toward a Female Alternative Vision of Power

 A Wild Patience Has Taken Me This Far (1981). What will be emphasized is the gradual shift that can be observed in Rich's work from "power" first conceived of as "power-as-force"-a category provided by Claire Keyes's reference study The Aesthetics of Power: The Poetry of Adrienne Rich (1986) and associated with a patriarchal society and our androcentric culture-, to a feminist and/or female conception, characteristic of the poet's radical feminism during the second-wave feminist era, more concerned with the values of change and care, or the forces of life. Particular attention will be paid to the notion of commitment in Adrienne Rich's work.

Dans cet article, il est question de la notion de "pouvoir" dans la poésie d'Adrienne

Rich et de l'évolution de l'approche de cette notion par la poète à travers ses trois premières décennies de création, de A Change of World (1951) à The Dream of a Common Language (1978) et A Wild Patience Has Taken Me This Far (1981). L'accent sera mis sur le passage que l'on peut observer dans l'oeuvre de Rich d'une conception du "pouvoir-en-tant-que-force"une catégorie élaborée par Claire Keyes dans son étude de référence The Aesthetics of Power : The Poetry of Adrienne Rich (1986) et associée à la société patriarcale et notre culture androcentrée -, à une conception féministe et/ou de femme, caractéristique du féminisme radical de la poète à l'heure de la deuxième vague féministe, plus concernée par les valeurs de changement et de soin, ou les forces de vie. Une attention particulière sera portée à la notion d'engagement dans l'oeuvre d'Adrienne Rich. The notion of "power" is a pivotal one in the poetry of Adrienne Rich, as revealed by the reference study The Aesthetics of Power: The Poetry of Adrienne Rich (1986) by critic and

father under whose tutelage she began writing. In this essay, Rich describes her discovery of language as a form of power which she then equated with the "ability," already at a very young age, to "share in" the poetic tradition, and the dominant aesthetics of her time in particular. Describing the influence of her father she declares: "He taught me . . . to believe in hard work, to mistrust easy inspiration, to write and rewrite; to feel that I was a person of the book, even though a woman; to take ideas seiously. He made me feel, at a very young age, the power of language and that I could share in it" (Rich,Blood,Bread,and Poetry 113).

Discovering and "sharing in" the power of language as a child, Rich began her career as a poet who adhered to the aesthetics elaborated by the Modernist poets and the representatives of American New Criticism, still prevailing in the mid-twentieth century.

At the beginning of the poet's career, "power" meant sharing the "ability" and "authority"-two levels of meaning of the Latin verb "potere"-of some of the most representative figures of the period and their belief that true and good poetry should be impersonal, universal, and, of course, apolitical. However, in Rich's poetry, power appears to be endowed with a remarkably protean quality, one which any attentive and consistent reader of her work is sooner or later challenged to consider. Indeed, how does power as the powerto-share-in the power of language, the power of those who detain cultural and, more particularly, poetic authority, evolve throughout the first three decades of the poet's creation, from A Change of World (1951) to the poetry of the late 1970s that will be the focus of the present study?

In her work published from the early 1960s onward, Adrienne Rich rejected most of the aesthetic positions elaborated by her Modernist predecessors as the symbol of dominant social values conveying a conservative and oppressive bourgeois ideology. Her poetry would gradually become an instrument calling the dominant social and political order into question.

It would also, even more radically, mean breaking with the dominant poetic tradition that she came to identify as male, most notably in the essay of feminist literary criticism "'When We Dead Awaken': Writing as Re-Vision" (1971). Another aspect of the evolution of Rich's approach to the notion of power will lead to considering the poet's feminist or female redefinition of power as a notion that substitutes the forces of life and of care, regarded as power, for a patriarchal conception of "power-as-force," a category introduced by Claire Keyes. Through the advent of a woman's voice and a woman's vision, through the exploration of a woman's position in the world and the rediscovery or the reassessment of women's cultural heritage, power, in Rich's poetry, becomes synonymous with "language as transforming power," a category introduced by the poet in the essay "Power and Danger: Works of a Common Woman" (1977) 1 -in other words, with the power of poetry to transform "patriarchal poetry"2 and the patriarchal order itself.

Writing or Sharing in the "power of the fathers"

As shown by the passage from "Split at the Root" quoted above, as an apprentice poet, Adrienne Rich had inherited the Modernist vision, derived from French Symbolism, of the poet as a "poïétès," from the Greek verb "poiein," "to make." From this perspective, poetry is a "discipline," the poet a technician who masters poetry conceived of as a matter of "craft."

This heritage goes back to the theories of "art for art's sake," to the belief, expounded by Edgar Allan Poe, for instance, in his famous essay "The Poetic Principle" (1850), that "there neither exists nor can exist any work more thoroughly dignified-more supremely noble than this very poem-this poem per se-this poem which is a poem and nothing more-this poem written solely for the poem's sake" (Poe 1435-36). In the early years of her career, Rich can be associated with a tradition of American poetry descending from Poe and Ralph Waldo Emerson-the latter in particular, independently from his revolutionary defense of the Americanization of American poetry, having theorized the split between poetry and politics several decades before the French Symbolist poets, as indicated by his famous "Ode, Inscribed to William H. Channing" (1846). In this poem, Emerson expresses his suspicion of the priest's jargon, the stateman's diatribe and "their politique": "Which at the best is trick" to the "angry Muse" (Emerson 65). Adrienne Rich's first two collections of poems, A Change of World (1951) and The Diamond Cutters (1955), show her adherence to the Modernist aesthetic belief in the autonomy of the work of art and of language itself, in the necessity to circumscribe language for the purpose of art, which still prevailed in the mid-twentieth century. They illustrate the poet's mastery of her poetic medium, a mastery praised by W. H. Auden who prefaced her first collection of poems, which he had personally chosen for the Yale Younger Poets Series.

In his foreword to A Change of World, Auden underlines Adrienne Rich's "craftsmanship," which "includes, of course, not only a talent for versification but also an ear and an intuitive grasp of much subtler and more difficult matters like proportion, consistency of diction and tone, and the matching of these with the subject at hand" (Rich, Poetry and Prose 340). He praises her for her "modesty, not so common at that age, which disclaims any extraordinary vision" and for the tribute her poems pay to her Modernist predecessors, Robert Frost, W. B. Yeats, T. S. Eliot, whose voices her poems resonate with. Last but not least, Auden emphasizes the presence in the young poet's work of "the evidence of a capacity for detachment from the self and its emotions without which no art is possible" (340), a statement directly echoing T. S. Eliot's well-known aphorism in the essay "Tradition and the Individual Talent" (1919), according to which "the emotion of art is impersonal." An heir to the Modernists, Adrienne Rich could not avoid the influence of American New Criticism3 either that established a method to interpret poetic texts which would have an influence on generations of poets, by ranking form over content, as well as by insisting on the timelessness and universality of poetic writing.

The poems published in Rich's first two collections are essentially composed metrically and show her expertise at composing in the iambic foot, sometimes even using the heroic couplet, though not systematically using the fixed forms of the poem inherited from the European tradition. They also undeniably possess an abstract or meditative quality without necessarily sounding excessively artificial to the reader familiar with her later work. It is easy to perceive the poet's keen intelligence and talent at assembling words melodiously, at composing poems that develop like abstract meditations, notably through the recourse to extended metaphors or elaborate comparisons, as immediately revealed by "Storm Warnings," the opening poem of A Change of World, where a parallel is drawn between "[w]eather abroad / And weather in the heart [which] alike come on / Regardless of prediction" (Rich, Poetry and Prose 3). Some poems are endowed with a pronounced metapoetic quality, showing the young poet's interest in theorizing the art of poetry, as exemplified by the poem "At a Bach Concert," in which poetry is presented as an "antique discipline," and "[a] toocompassionate art" is seen as "only half an art" (Rich, Poems. Selected andNew, 1950-1974 7), a statement that once more conjures up T. S. Eliot's theory of the superiority of impersonality in poetry; as also illustrated by the eponymous poem of her second collection, "The Diamond Cutters," which amazingly resonates with Théophile Gautier's "ars poetica" embodied within the poem "L'Art" at the very end of Émaux et Camées (1852). In this title poem, also the final poem of Rich's collection, in which the poet, like her French predecessor, uses the metaphor of statuary to turn the poet into a skilled expert at questions of form, one reads a series of injonctions through which poetry is equated with the practice of an erudite literary elite, such as: "Be serious, because / The stone may have contempt / For too familiar hands" ; or else "Be hard of heart," "Be proud, when you have set / The final spoke of flame" (Rich, Poetry and Prose 7-8).

From the perspective of American feminist literary criticism, and in particular of Elaine Showalter's theory of the three phases-"Feminine, Feminist, Female"-of a tradition of literature by women expounded in A Literature of Their Own: British Novelists from Charlotte Brontë to Doris Lessing (1978), the poet's attitude, while showing some selfassuredness, can be regarded as "feminine." In other words, to quote Elaine Showalter's study, it is marked by the "imitation of the prevailing modes of the dominant tradition, and internalization of its standards of art" (11). In order to be recognized as a true poet by those who are endowed with the authority or the power to determine the acceptability of a subject or the quality of a poem, the young poet had no choice but to conform to and adopt the dominant aesthetic beliefs of her time. To repeat Suzanne Juhasz's words in the feminist essay Naked and Fiery Forms: Modern American Poetry by Women (1976), when commenting on the achievements of Modernist women poets, Adrienne Rich could not avoid playing "by the boys' rules" (4). In "Poetry and Experience: Statement at a Poetry Reading" (1964), Rich would later describe "control, technical mastery and intellectual clarity" as "the real goals" in her first books of poems (Rich, Poetry and Prose 181), while in "'When We Dead Awaken': Poetry as Re-Vision," her groundbreaking essay of poetic introspection and feminist literary criticism applied to poetry, she would insist that: "[her] style was formed first by male poets: by the men [she] was reading as an undergraduate" (Rich, Poetry and Prose 187). She was simultaneously "sharing in" the power of the mighty ones under patriarchy, since cultural authority has traditionally been synonymous with political and social dominance. The mastery of linguistic discourse has always been a form and an instrument of power, "power-as force," to use the category provided by Claire Keyes to designate the prevailing idea of power under patriarchy.

Poetry and Commitment: The Transforming Power of Poetry

The 1960s were years of tremendous changes in the life and work of Adrienne Rich, then a married woman who had brought three sons into the world before turning thirty. They were years of growing social consciousness and of political commitment, a central issue for the poet as emblematically revealed in Poetry and Commitment (2007), a text initially given as a plenary lecture at the Conference on Poetry and Politics of 2006 at Stirling University, Scotland. In this lecture, Rich explores the relationship between two notions that the Symbolist poets in the nineteenth century and Modernist poets at the turn of the twentieth century chose to oppose by simultaneously rejecting the Romantic belief in the mission of the poet, be it moral, didactic, or political. In this text, the poet, "scanning the terrain of poetry and commitment" (Rich, Poetry and Commitment 5), draws attention to a tradition of poets who, from Percy Bysshe Shelley to the Scottish Marxist bard Hugh MacDiarmid, to the Greek Communist poet Yannis Ritsos, and to the South African anti-apartheid poet Dennis Brutus, took the opposite view of modern poets by rejecting the split between poetry and politics and considering it the duty of the poet "to be concerned about the politics of [his/her] country" (Rich, Poetry and Commitment 9).

In the late 1960s, Adrienne Rich became a political person, an activist, and began to write "political poetry." The essay "Split at the Root: An Essay on Jewish Identity" testifies to the poet's involvement in the Civil Rights Movement, when she writes, for instance, that: "Most of the political work [she] was doing [in those years] was on racial issues, in particular as a teacher in the City University during the struggle for open admissions." (Rich,Bread,Blood,and Poetry 119). In 1968, Adrienne Rich started working for the SEEK (Search for Education, Elevation, and Knowledge) program for disadvantaged young people at City College of New York, an experience retraced in the essay "Teaching Language in Open Admissions" (1972). As a poet-teacher involved in the open admissions struggle, Rich's "job" with "black and Puerto Rican freshmen from substandard ghetto high schools" was "'to turn the students on' to writing by whatever means [she] wanted-poetry, free association, music, politics, drama, fiction-to acclimate them to the act of writing, while a grammar teacher with whom [she] worked closely outside of class, taught sentence structure, the necessary mechanics" (Rich, On Lies, Secrets, and Silence 55).

Rich's commitment to and support of the Civil Rights and Peace movements reverberate in many poems of the period as a whole new attitude emerging in her work. It was an attitude that revived the political stance advocated by Walt Whitman, the first and one of the most political American poets, as emphasized by Whitman scholars like Betsy Erkkila;

Whitman indeed positioned himself as the "bard of democracy" in its radical, egalitarian and proletarian version, throughout the poems of his monumental Leaves of Grass. To Whitman, the poet fails "[i]f he does not flood himself with the immediate age . . . and if he be not himself the age transfigured," as written in the 1855 Preface to Leaves of Grass (633). For him, just as for Percy Bysshe Shelley, one of the "revolutionary-minded" poets in Rich's own words (Poetry and Commitment 6), "Presidents shall not be [the people's] common referee so much as their poets shall" (Whitman 619). Whitman started writing during the American Romantic period, which critics agree spanned a period of fifty years, between approximately 1810 and 1865. He started writing at the tail end of European Romanticism, which was placed under the sign of "Revolutions." The question of the relationship between English Romantic poets and their revolutionary historical context, the radical positions of William Blake, for instance, and the revolutionary ideas of Samuel Taylor Coleridge, have been often commented upon. Unlike his British counterparts, Whitman never really lost his faith in revolution, his admiration for the French Revolution, nor his faith in agitation and revolt, due to his belief in a radical form of democracy.

Rich's poetry of the midand late 1960s seems to be particularly in tune with the positions of her anglophone Romantic predecessors for whom "there was no contradiction among poetry, political philosophy, and active confrontation with illegitimate authority" (Rich, Poetry and Commitment 6). It is interesting, moreover, to draw a parallel between her political stance and Jean-Paul Sartre's theory of commitment in literature expounded in Qu'est-ce que la littérature? (1948). And this even though, as underlined by Benoît Denis in Littérature et engagement: De Pascal à Sartre (2000), the existentialist philosopher and novelist does not consider the genre of poetry as particularly compatible with commitment, which he essentially associates with prose. Indeed, as can be read in the chapter "Qu'est-ce qu'écrire?" at the beginning of Sartre's essay, to him: "poets are men who refuse to use language" (Sartre 17, my translation). 4 The purpose of this article is not to discuss Sartre's viewpoint regarding poetry and commitment, but rather to show the particular resonance of the philosopher's conception of the "committed" writer in Rich's work, despite his ideas about poetry. To Sartre, the aesthetic aim cannot be sufficient in and of itself. In his essay, he emphasizes, for instance, that "the function of the writer is to act in such a way that no one can be ignorant of what happens in the world and that no one may say that he did not know" 5 (Sartre 31, my translation). To him, writing means to "disclose" the world in order to "change," to transform it, through the power of language: "The 'committed' writer knows that words are action: he knows that to reveal is to change" 6 (Sartre 30, my translation). One knows the importance of the notion of "change," which is in fact intertwined with that of "power" in the poetry of Adrienne Rich. In Rich's poetry written around 1968, power gradually becomes synonymous with the power to break with the pretension to neutrality and universality of the Modernist tradition and the advocates of American New Criticism. In "Poetry and Commitment," she goes as far as to declare: "There is no universal Poetry …, only poetries and poetics, and the streaming, intertwining histories to which they belong" (Rich, Poetry and Commitment 21). To her, integrating social and political issues into poetry was becoming a "necessity," as evidenced by the eponymous poem of her 1966 collection, Necessities of Life. In this poem, the speaker in the act of metaphorically giving birth to herself again declares that "[she]'ll // dare inhabit the world / trenchant in motion as an eel, solid // as a cabbage-head" (Rich, Poetry and Prose 18).

Adrienne Rich gradually developed a belief in the responsibility of the poet and in poetry as an instrument to act upon the world, as revealed by the essay "Blood, Bread, and Poetry: The Location of the Poet" (1987), in a passage in which she introduces herself as belonging to a community of American poets sharing her own growing political stance: . . . I was writing at the beginning of a decade of political revolt and hope and activism. The external conditions for becoming a consciously, self-affirmingly political poet were there, as they had not been when I had begun to publish a decade earlier. Out of the Black Civil Rights movement, amid the marches and sit-ins in the streets and on campuses, a new generation of Black writers began to speak-and older generations to be reprinted and reread; poetry readings were infused with the spirit of collective rage and hope. As part of the movement against United States militarism and imperialism, white poets also were writing and reading aloud poems addressing the war in Southeast Asia. In many of these poems you sensed the poet's desperation in trying to encompass in words the reality of napalm, the "pacification" of villages, trying to make vivid in poetry what seemed to have minimal effect when shown on television. (Rich,Blood,Bread, The poet's voice in this passage echoes those of many of her contemporaries, and in particular that of Denise Levertov who expounded her conception of "political poetry" in the essay "On the Edge of Darkness: What is Political Poetry" (1975) published in the collection of essays Light Up the Cave (1981). Like Rich in the passage quoted above, Levertov provides an approach to the power of "political poetry" which she describes as capable of "indirectly hav [ing] an effect upon the course of events by awakening pity, terror, compassion and the conscience of leaders" (168).

The political quality of the poetry of Adrienne Rich, who did not fear the reticence and criticism of those who saw an inherent contradiction between the spheres of poetry and politics, is most explicitly illustrated in Leaflets: Poems 1965Poems -1968Poems (1969)). In this collection, such poems as "To a Russian Poet," written in support of the dissident poet Natalya Gorbanevskaya confined to a psychiatric hospital after participating in a demonstration to protest against the invasion of Czechoslovakia by the Soviet Union 7 , and "Jerusalem," resonating with the war opposing Palestinians and Israeli, appear to be inseparable from political issues and their political context. As for the poem "To Frantz Fanon," written in homage to the West Indian Marxist theorist of colonization, it can be regarded as one of the poems of the period most explicitly showing the poet's hostility to colonialism and racism. In Part III of Leaflets, in the long sequence poem "Ghazals: Homage to Ghalib," the classical poet from India who wrote in Urdu and in Persian, who was a witness to the establishment of the British Colonial Rule in India and of British colonialism in the nineteenth century, one finds, for instance, the statement: "Last night you wrote on the wall: Revolution is poetry" (Rich, The Fact of a Doorframe 107). Such a poem, which revisits the traditional ghazal form 8 , also draws our attention to the deeply experimental quality of the poetry of the period, which will be tackled further down. Composed during the same decade as the poems included in Leaflets, the poem "Tear Gas" seems to bear witness to the poet's activism, providing an example of her writing emanating from her involvement in the anti-war protest. This is emphasized by the epigraph that introduces the circumstances that prompted the composition of the poem: "(October 12, 1969: reports of the tear-gassing of demonstrators protesting the treatment of G.I. prisoners in the stockade at Fort Dix, New Jersey)." The opening line of the poem also immediately refers to some form of activism: "This is how it feels to do something you are afraid of. / That they are afraid of" (Rich, Poems. Selected andNew, 1950-1974 139).

From this point on, Adrienne Rich's poems will be endowed with a two-fold political dimension questioning both her mentors' positions on the social function of poetry and American mainstream politics. The collection of poetry which best conveys this double attitude may well be The Will to Change, the poet's sixth collection, published in 1971.

The political and experimental breadth of the poems collected in The Will to Change, influenced by the revolutionary poetics of Charles Olson's "theory of projective verse," an influence commented on in detail by Claire Keyes in her essay, is particularly noticeable in "The Burning of Paper Instead of Children." One of the major poems of the book, in which Adrienne Rich "will not create any polished form; [in which] she will do away with 'form' in the old sense-and work with her 'notes'" (Keyes 123), "The Burning of Paper Instead of Children" echoes the poet's involvement against the Vietnam War and brings into relief her 7 For more details on the poet's relation to Natalya Gorbanevskaya and analysis of the kind of oppression that women are subjected to under patriarchy, see "Caryatid: Two Columns" in On Lies, Secrets andSilence: Selected Prose 1979-1985 (116-19). 8 The ghazal is a lyric love poem which originated in Arabia in the sixth century before spreading to Persia and India. It is composed of couplets characterized by the repetition of the same word or group of words rhyming at the end of each second line throughout the poem. belief in the responsibility of the artist and his or her mission to act upon the world through the power of words. The prose paragraph which opens the long free verse poem made of five interrelated sections and a total of ninety-seven lines, reads as an illustration of the interpenetration of the personal and the political, one of the essential characteristics of the political vein in Rich's poetry:

1. My neighbor, a scientist and art-collector, telephones me in a state of violent emotion. He tells me that my son and his, aged eleven and twelve, have on the last day of school burned a mathematics textbook in the backyard. He has forbidden my son to come to his house for a week, and has forbidden his own son to leave the house during that time. "The burning a book," he says, "arouses terrible sensations in me, memories of Hitler; there are few things that upset me so much as the idea of burning a book." (Rich, Poetry and Prose 34)

In this introductory section, a parallel is drawn by one of the speaker's neighbors between the burning of a "mathematics textbook" and the tragic episode of Nazism. The reference to the traumatic events of contemporary history conjures up the words of critic M. L. Rosenthal in

The New Poets: American and British Poetry Since World War II (1967): "War is more than a theme or subject for modern writers. It is a condition of consciousness, a destructive fact that explodes within the literature as without it" (410). For the critic "many poets are grappling with a world fundamentally changed by the holocaust." The poem "The Burning of Paper Instead of Children," however, is more immediately and deeply rooted in the historical context of 1968, the year of its composition. The poem was actually written from the height of the turmoil and the violence of the Vietnam War, and the title immediately rings like an allusion to the napalm burning of Vietnamese villages. The violence of the war will be directly targeted in the fifth and last section of the poem, another prose paragraph and a response of sorts to the opening one, which reads as a radical critique of the language at the disposal of the poet necessarily engaged in a process of transformation: I know it hurts to burn. There are flames of napalm in Catonsville, Maryland. I know it hurts to burn. The typewriter is overheated, my mouth is burning, I cannot touch you and this is the oppressor's language. (Rich, Poetry and Prose 37)

The energy of active protest against the war in Vietnam is omnipresent in the text as an essential background, even though the issues of social injustice and of poverty are also raised in "The Burning of Paper Instead of Children." In section three, in one more prose paragraph "written [this time] by one of Rich's students in the Open Admissions Program at City College of New York," as specified in a footnote and suggested by several grammatical mistakes, one reads that "People suffer highly in poverty and it takes dignity and intelligence to overcome this suffering. Some of the suffering are: a child did not had dinner last night: a child steal because he did not have money to buy it: to hear a mother say she do not have money to buy food for her children and to see a child without cloth it will make tears in your eyes." (Rich,Poetry and Prose,35) The poems of the 1971 collection The Will to Change cannot be read as propaganda and "remain poems," as emphasized by Albert Gelpi in the essay "Adrienne Rich: The Poetics of Change" (Rich, Poetry and Prose 292-298). They draw the reader's attention to the importance of the notion of "sight," of "vision," acting as the metaphor for the quest for awareness, for becoming aware of the assumptions, the values and beliefs, which determine and limit an individual's existence and position in the world and, more particularly, women's existence in a patriarchal society. Like the image of the "camera" in the poem "Diving Into the Wreck," the title poem of the 1973 collection marking the breakthrough to a feminist poetics in Rich's work, the poems gathered in The Will to Change draw attention to the quest for awareness concerning "sexual politics" or, in other words, from Kate Millett's perspective in Sexual Politics, "a set of stratagems designed to maintain a system" in which male ascendency operates and is ensured under the institution of patriarchy (Millett 23). As Kate Millett elaborated her theory of patriarchy as a system in which men possess power over women in all fields, the issue of power relations between the sexes was to become a key focus in Rich's poetry.

The Powerful Language of Women's Powerlessness

Years of commitment in the poet's life and work, the 1960s were also a decade during which the poet began to consider her experience in society as gendered and as inseparable from the wider situation of women in a society identified as patriarchal. The publication of Snapshots of a Daughter-in-Law in 1963, eight long years after the publication of The Diamond Cutters, had already constituted a watershed in the poet's career. It coincided with the emergence of the Women's Liberation Movement in the United States, marked by the coming out, the same year, of Betty Friedan's groundbreaking sociological essay The Feminine Mystique, which threw light onto "the problem which [had] no name" (the title of the opening chapter of the book) and gave a voice to thousands of white American middle-class women feeling trapped in "the new religion of femininity and the Wife-Mother goddess," as emphasized by Ginette Castro in American Feminism: A Contemporary History (14-15). At the end of World War II, with the return of the G.I.s, and hence the return of a male workforce, the idea that "a woman's place is in the home" was back into circulation.

Most middle-class American women were once more confined to the traditional role of housewife and mother, even though many among them had graduated from high school or from college and could legitimately aspire to a profession. Betty Friedan's book, which was one of the first attacks on the conservatism of Freudian theories regarding "femininity," as underlined by feminist critics and historians, had the effect of a catharsis for many of its female readers.

Moreover, as can be read in "Blood, Bread and Poetry," Rich's third collection Snapshots of a Daughter-in-Law had coincided with the poet's beginning to write "directly and overtly as a woman, out of a woman's body and experience, to take women's existence seriously as theme and source for art"; it had coincided with her beginning to feel "for the first time the closing of the gap between woman and poet" (Rich, Blood, Bread, and Poetry 182).

From the perspective of feminist literary criticism, she was overcoming the traditional antagonistic relationship between "poet" and "woman," one first theorized in A Room of One's Own (1929) by Virginia Woolf, in the now widely quoted parable about the tragic lot of Judith Shakespeare, Shakespeare's imaginary sister. According to Susan Stanford Friedman in the essay "Adrienne Rich and H. D.: An Intertextual Study," the author of Snapshots of a Daughter-in-Law was "gradually changing from a poet who had erased all traces of gender to one who explored the dailiness of a woman's life" (qtd. in Cooper 174). In her third collection, in the eponymous poem more particularly, Rich began to explore the situation of the female artist and, more broadly, of all women in the ultraconservative post-World War II American society, in which true womanhood was equated with marriage and motherhood, a limitative norm arousing in many women a feeling of powerlessness. 9

The issue of the experience of powerlessness in the institutions of patriarchal marriage and motherhood runs throughout the poems of Necessities of Life (1966) and Leaflets (1969), some of which are endowed with a particularly personal vein reminiscent of the poetry of 9 In her study of American feminism, Ginette Castro comments on the fact that the post-World War II period, with all its conservatism, saw the appearance of a new societal problem, "the housewife's syndrome," designated as such by historians, by psychologists, and in the media. The problem, regarded as a kind of "epidemic," as "a national catastrophe," was taken so seriously that a sociologist, Ferdinand Lundberg, and a psychologist, Marynia Farnham, devoted a study to it: Modern Woman: The Lost Sex (1947). In this study, which became a best-seller, the women suffering from the so-called syndrome were stigmatised as "neurotic" and as showing the symptoms of "feminist illness." American confessional poets, and in particular of the voices of Adrienne Rich's female counterparts, Sylvia Plath and Anne Sexton. In these two collections, poems abound which show the lyrical self's attempt to relate the experience of women confined in the patriarchal matrimonial system with their situation of exclusion from the public sphere. These collections of poems resonate with Simone de Beauvoir's analysis in The Second Sex, echoes and reverberations of which could already be found in "Snapshots of a Daughter-in-Law." Poems on the speaker's sense of powerlessness and, even more radically, on the exploration of the destructiveness generated by the limits imposed on the female subject by traditional female roles, are recurrent in Leaflets. This is revealed by poems such as as "Night Watch," "Picnic,"

or "Implosions," and most strikingly by "Orion," the opening poem of the 1969 collection. In "Orion," lines such as "Indoors I bruise and blunder" or "A man reaches behind my eyes / and finds them empty," are emblematic of the poet's "necessity for life," as emphasized by Albert Gelpi, for her own survival, "of re-ordering social values and structures" (Rich, Poetry and Prose 293). And yet, as revealed by deeply personal poems, by a poem such as "Orion," which refers at once to a constellation and to Greek mythology, the poet's commitment to the social function of poetry always involves the elaboration of striking and powerful images, particularly skillful linguistic and stylistic choices, a deep concern with form and with the experimentation with new forms, a characteristic of the poet's artistry in all her "political poetry."

From a Feminist to a Female Alternative Vision of Power

At the beginning of The Will to Change, in the poem "Planetarium," one of the poems opening the collection and which resonates with the poet's involvement as a theorist and activist in the Women's Liberation Movement, Rich's poetry positions itself as deliberately invested with a mission, a metaphorically "archeological" one. It will consist in rediscovering the memory of women whose names have been erased from History, also "his" story, as pointed out in American feminist criticism. Written while "[t]hinking of Caroline Herschel, 1750-1848, astronomer, sister of William; and others," "Planetarium" can be read as a tribute to all women stigmatized or persecuted for audaciously breaking with women's traditional social roles: 10 a woman "in the snow among the Clocks and instruments or measuring the ground with poles" in her 98 years to discover 8 comets she whom the moon ruled like us levitating into the night sky riding the polished lenses Galaxies of women, there doing penance for impetuousness ribs chilled in those spaces of the mind (Rich, The Will 13)

In "Planetarium," where the poet dares to use the first-person pronoun "I" pointing to herself as at once a circumstancial self and a political subject, the voice becomes overtly committed to the rediscovery of women's accomplishments as a response to the prevaling ideology equating true femininity with self-abnegation and renunciation: . . . I am an instrument in the shape Of a woman trying to translate pulsations Into images for the relief of the body And the reconstruction of the mind. (Rich, The Will 14)

In a vibrating and visionary statement, the poet inaugurates her new mission, one very similar-in its poetic version of impressive body and cosmic imagery and of quest for a new poetic language-, to the commitment of numerous scholars and critics, historians and publishers in the last fifty years, to recover the forgotten history of women's creations in all its diversity. 11 This mission will be carried on in Adrienne Rich's next collection, whose eponymous poem, "Diving Into the Wreck," can be read as the expression of the poet's radical position as the explorer, among a community of women, of a patriarchal society and of our androcentric culture metaphorically represented as a "wreck": I came to explore the wreck. The words are purposes. The words are maps. I came to see the damage that was done. . . . 11 One of the best instances of this kind of commitment can be found in a recent publication: Dictionnaire Universel des Créatrices, eds. Béatrice Didier, Antoinette Fouque, Mireille Calle-Gruber (Paris : Des femmes-Antoinette Fouque, 2013).

We are, I am, you are by cowardice or courage the one who find our way back to this scene carrying a knife, a camera a book of myths in which our names do not appear. (Rich,Poetry and Prose 44) If in this poem, as underlined by Claire Keyes, the poet still sees "[the] androgynous ideal as a vision of human wholeness and the health of the race" (Keyes 133), as revealed, for instance, by the central affirmation "I am she: I am he," nevertheless, in the essay "Caryatid : Two Columns," published the same year as Diving Into the Wreck (1973) 12 , she provides a theoretical complement to her poetic stance. From a feminist perspective, she declares: "We need a poetry which will dare to explore, and to begin exploding, the phallic delusions which are now endangering consciousness itself" (Rich, On Lies, Secrets, and Silence 116). The reconstruction of a female memory, if it leads to the reassessment of women's power through the rediscovery of the creations of women of note, may also lead to a new approach to the notion of power itself: to an alternative to the definition of "power-as-force" in the "Kingdom of the Fathers" (Rich, Of woman Born 56).

The rediscovery and reappropriation of women's cultural heritage and, to begin with, of the accomplishments and creations of reputable women, characterize Adrienne Rich's poetry of the 1970s, as most explicitly revealed by the poem "Power" dedicated to Marie Curie, and placed at the very beginning of the collection The Dream of a Common Language (1978). It is now well-known that Marie Curie, who had discovered the vital properties of radium and was awarded two Nobel Prizes for her research on radiation phenomena, died from radiation poisoning, as alluded to in the last lines of the poem: She died a famous woman denying her wounds denying her wounds came from the same source as her power (Rich, The Dream 3) Is the implicit equation of "power" and death, in this "hesitant, ambivalent poem in its handling of Marie Curie," to repeat Lynda K. Bundtzen's words (qtd. in Jones 46), a way of calling into question scientific "power" when it is unscrupulously instrumentalized by powerful nations? Is "power" according to the dominant patriarchal ethos called into question here? In the article "Power and Poetic Vocation in Adrienne Rich's The Dream of a Common Language," Lynda K. Bundtzen actually mentions the tragic consequences of the appropriation of Marie Curie's contribution to the study of radium and raditation for military purposes, which led to the invention and tragic use of the atomic bomb during World War II, as well as to the arm race of the Cold War and other disastrous situations. And yet, even though Marie Curie could neither master nor control the tragic impact of her descoveries, she may nevertheless stand as a symbol of the traditional, cultural dedication of women to the forces of life against the culture of war, identified by Rich and other radical feminists, especially the ones associated with the differentialist pole of second-wave feminism, as one of the trademarks of male-dominated society. During World War I, the scientist's research enabled her to courageously promote the use of X-rays on the battlefields, to help surgeons operate on the wounded soldiers. Dedicated to an exceptional woman who was committed to the forces of life, "Power" is also symbolically placed at the beginning of a collection of poetry that exudes with the utopian spirit and the political drive to "change the world" which marked the 1970s. It is emblematic of the elaboration, by some radical feminist thinkers and poets of the period, of a renewed vision of life and of an alternative ethics standing in sharp contrast to the patriarchal dominant values of authority, hierarchy, competition or "competitiveness" (a notion clearly called into question in the poem "Transcendental Etude" in particular), and designating the domination of women by men as a template for all the other forms of domination (see Ramond). Adrienne Rich's poem, while celebrating the intellectual power of an exceptional woman, seems to provide the vision of an alternative definition of power, one identified with the positive values of care and solidarity.

In The Dream of a Common Language, the poet will explore the revolutionary possibilities for solidarity between women presented as "sisters," and the collection echoes with the works of other feminist poets and activists, like Robin Morgan's groundbreaking anthology of feminist theory Sisterhood is Powerful (1970), whose title was turned into a slogan. In Adrienne Rich's poetry of the 1970s, the figure of the sister emerges as particularly significant and central, be it the real biological blood sister, as in the poem "Sibling Mysteries," or the symbolic one sharing a similar experience in patriarchal society and a similar quest for "a change of world." Gradually, Adrienne Rich's poetry will come to depict women acting together, supporting each other, as can be observed in "Phantasia for Elvira Shatayev" (Rich, Poetry and Prose 60-61) which tells the story of a Russian women's

Cf. On Lies, Secrets, and Silence. Selected Prose 1966-1978. As for Claire Keyes, she introduces the notion of "power-to-transform" in her study.

To paraphrase Gertrude Stein in her poem "Patriarchal Poetry."

New Criticism started with a group of conservative Southern scholars and formalist poets, for whom poetry was an art valuable for its own sake that was not supposed to serve any extrinsic purpose.

"Les poètes sont des hommes qui refusent d'utiliser le langage"

"la fonction de l'écrivain est de faire en sorte que nul ne puisse ignorer le monde et que nul ne s'en puisse dire innocent"

"L'écrivain 'engagé' sait que la parole est action : il sait que dévoiler c'est changer."

Still an issue in contemporary debates and publications as revealed, for instance, by the essay Sorcières : La puissance invaincue des femmes (2018) by Mona Chollet.

In the second section of the essay entitled "Vietnam and Sexual Politics".

climbing team led by Elvira Shatayev, "all of whom died in a storm on Lenin Peak" in August 1974, as indicated by the poet in the epigraph. In this poem, written from Elvira Shatayev's viewpoint, the figure of the symbolic sister and the concept of sisterhood as synonymous with union and power regained by women, are essential. Women's acting together, their supporting each other, is then presented as an audacious and revolutionary response to a society organized to serve men's needs and which has traditionally conceived of women's relationships in terms of rivalry, of competition and alienation from each other; a situation that the first two waves of feminism strove to overcome, but that the popularization of mainstream psychoanalytic theories of "femininity," as underlined by Kate Millett in Sexual Politics, reinforced. As emphasized by Judith McDaniel in the essay "'Reconstituting the World': The Poetry and Vision of Adrienne Rich," such a poem as "Phantasia for Elvira Shatayev," as well as the group of love sonnets "Twenty-One Love Poems" placed at the centre of the 1978 collection, provide "a glimpse of the power generated by love, specifically the love of women for women" (Rich, Poetry and Prose 365).

What is noteworthy and must be underlined is that Adrienne Rich would gradually complement the rediscovery of female scientists, literary or artistic figures, whose experience she could compare to her own, with the reassessment of and a tribute paid to the unwritten, unrecorded, discredited experiences or culture of anonymous women, the traditionally invisible and ignored. Written from an overtly feminist and female perspective, Rich's volumes of poetry The Dream of a Common Language and A Wild Patience Has Taken Me This Far (1981) strive to restore the value of a female culture marked, since time immemorial, by the transmission of life and a privileged relation to its preservation reappropriated by women themselves. In Rich's poetry of the 1970s and early 1980s, women's culture of the preservation of life and care taking is turned into a sort of "counter-culture" or "counterpower" to the masculine institutionalization of "power-as-force." In the long poem "Natural

Resources" placed at the end of The Dream of a Common Language, breaking with the notion of androgyny presented in Diving Into the Wreck as a response to binary gender oppositions and the traditional denigration of the feminine and the female in our androcentric culture, in section 13: There are words I cannot choose again: humanism androgyny Such words have no shame in them, no diffidence Before the raging stoic grandmothers (Rich, The Fact of a Doorframe 262)


Arthur Alexandre

Maxime Lavaud

Nicolas Fares

Elodie Millan

Yann Louyer

Thomas Salez

Yacine Amarouchene

Thomas Guérin

David S Dean

Non-Gaussian diffusion near surfaces

We study the diffusion of particles confined close to a single wall and in double-wall planar channel geometries where the local diffusivities depend on the distance to the boundaries. Displacement parallel to the walls is Brownian as characterized by its variance, but it is non-Gaussian having a nonzero fourth cumulant. Establishing a link with Taylor dispersion, we calculate the fourth cumulant and the tails of the displacement distribution for general diffusivity tensors along with potentials generated by either the walls or externally, for instance gravity. Experimental and numerical studies of the motion of a colloid in the direction parallel to the wall give measured fourth cumulants which are correctly predicted by our theory. Interestingly, contrary to models of Brownian-yet-non-Gaussian diffusion, the tails of the displacement distribution are shown to be Gaussian rather than exponential. All together, our results provide additional tests and constraints for the inference of force maps and local transport properties near surfaces.

The transport properties of colloidal particles in complex media can be very different from those observed in simple fluids. In the bulk of simple fluids, beyond molecular length and time scales, the motion of a colloidal particle satisfies two important properties: (i) its Mean Squared Displacement (MSD) increases linearly with time (diffusive behavior) and (ii) the probability distribution functions (PDF) of position increments are Gaussian. In complex media, exhibiting dynamical and spatial heterogeneities, or in presence of flows or active forces, both properties (i) and (ii) are generally not satisfied. Examples range from non-Gaussian transport in hydrodynamic flows, with consequences for chemical delivery in microfluidic environments [START_REF] Aminian | How boundaries shape chemical delivery in microfluidics[END_REF], to experimental observations of anomalous diffusion in complex fluids and biological media [START_REF] Bressloff | Stochastic models of intracellular transport[END_REF][START_REF] Höfling | Anomalous transport in the crowded world of biological cells[END_REF][START_REF] Ernst | Fractional brownian motion in crowded fluids[END_REF][START_REF] Tolić-Nørrelykke | Anomalous diffusion in living yeast cells[END_REF][START_REF] Shen | Single particle tracking: from theory to biophysical applications[END_REF].

Colloidal dynamics in a large class of complex media can be described as either Fickian-yet-non-Gaussian, anomalous-yet-Brownian or Brownian-yet-Non-Gaussian Diffusion (BNGD). [START_REF] Wang | Anomalous yet brownian[END_REF][START_REF] Wang | When brownian diffusion is not gaussian[END_REF][START_REF] Skaug | Intermittent molecular hopping at the solid-liquid interface[END_REF][START_REF] Leptos | Dynamics of enhanced tracer diffusion in suspensions of swimming eukaryotic microorganisms[END_REF][START_REF] Guan | Even hard-sphere colloidal suspensions display fickian yet non-gaussian diffusion[END_REF][START_REF] Chakraborty | Disorder-induced fickian, yet non-gaussian diffusion in heterogeneous media[END_REF]. These terms all refer to processes with linear-in-time MSDs but non-Gaussian PDFs, usually having exponential tails. A generic explanation for this phenomenon is the diffusing-diffusivity mechanism Ref. [START_REF] Chubynsky | Diffusing diffusivity: A model for anomalous, yet brownian, diffusion[END_REF]. In this scenario, BNGD is generated by a fluctuating diffusion constant, arising for example from fluctuations of the local density or of the gyration radius of complex macromolecules [START_REF] Yamamoto | Universal relation between instantaneous diffusivity and radius of gyration of proteins in aqueous solution[END_REF]. The diffusingdiffusivity mechanism has been further explored [START_REF] Chechkin | Brownian yet non-gaussian diffusion: from superstatis-tics to subordination of diffusing diffusivities[END_REF][START_REF] Sposini | First passage statistics for diffusing diffusivity[END_REF][START_REF] Lanoiselée | Diffusionlimited reactions in dynamic heterogeneous media[END_REF][START_REF] Lanoiselée | A model of nongaussian diffusion in heterogeneous media[END_REF][START_REF] Jain | Diffusion in a crowded, rearranging environment[END_REF][START_REF] Jain | Diffusing diffusivity: survival in a crowded rearranging and bounded domain[END_REF][START_REF] Yin | Non-gaussian normal diffusion in low dimensional systems[END_REF][START_REF] Miotto | Length scales in brownian yet non-gaussian dynamics[END_REF][START_REF] Hidalgo-Soria | Hitchhiker model for laplace diffusion processes[END_REF], but in most studies the assumptions invoked for the dynamically evolving diffusivity are generic but rather phenomenological. To the best of our knowledge, with the exception of the Brownian motion of an ellipsoidal particle [START_REF] Han | Brownian motion of an ellipsoid[END_REF][START_REF] Munk | Effective perrin theory for the anisotropic diffusion of a strongly hindered rod[END_REF][START_REF] Czajka | Effects of hydrodynamic interactions on the near-surface diffusion of spheroidal molecules[END_REF], there is currently no experimental realization of a system exhibiting fluctuating diffusivity at all times where the local diffusivity is quantified both experimentally, numerically and theoretically over broad spatial and temporal ranges.

In this Letter, we study the non-Gaussian diffusive motion of a colloidal particle near a hard wall. Hydrodynamic interactions at walls strongly modify the stochastic motion of neighboring objects [START_REF] Felderhof | Effect of the wall on the velocity autocorrelation function and long-time tail of brownian motion[END_REF][START_REF] Elgeti | Physics of microswimmers-single particle motion and collective behavior: a review[END_REF][START_REF] Jeney | Anisotropic memory effects in confined colloidal diffusion[END_REF][START_REF] Huang | Effect of interfaces on the nearby brownian motion[END_REF][START_REF] Choudhury | Active colloidal propulsion over a crystalline surface[END_REF][START_REF] Hertlein | Direct measurement of critical casimir forces[END_REF][START_REF] Helden | Direct measurement of thermophoretic forces[END_REF]. The local diffusivity parallel to the wall depends on the distance to the wall which itself fluctuates due to diffusion perpendicular to the wall, thus generating the diffusing-diffusivity mechanism. Note that a similar situation was previously considered in Ref. [START_REF] Matse | Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics[END_REF], but that study mainly focused on the motion perpendicular to the wall: in this case, the non-Gaussian behavior due to diffusing diffusivity can be observed only at small times, since at long times the presence of an interaction potential with the wall induces non-Gaussian displacements -even for uniform diffusivity. Furthermore, the non-Gaussianity of the motion in the parallel direction could not be resolved in Ref [START_REF] Matse | Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics[END_REF]. Here, we focus on the motion parallel to the wall which is a genuine realization of diffusing diffusivity at all times. Our theoretical analysis identifies a formal link with Taylor dispersion. In particular, we provide a calculation, that we verify experimentally and numerically, of the fourth cumulant of the displacement along the walls, which quantifies non-Gaussianity at all times. We also show that the tails of the PDF are Gaussian rather than exponential.

Physical model. We consider a Brownian particle of radius a that is confined between two walls separated by a distance 2H p , as shown in Fig. 1. The particle diffuses along the channel (i.e. the x-axis) and perpendicularly to it (i.e. the z-axis) with respective height-dependent diffusion coefficients D ∥ (z) and D ⊥ (z), and is subject to a potential V (z). The probability density p(z, t) about z at time t thus obeys the Fokker-Planck equation ∂ t p = -Hp(z, t), where

H• = - ∂ ∂z D ⊥ (z) ∂ ∂z • +β ∂V (z) ∂z • , (1)
with β = 1/(k B T ), where k B is Boltzmann's constant and T is the temperature. We assume no-flux conditions at the walls. In the long-time limit, the system equilibrates along the z direction and attains a Gibbs-Boltzmann distribution (see Fig. 2(a)):

p 0 (z) = e -βV (z) H -H e -βV (z ′ ) dz ′ . (2)
We denote by Z t ∈ [-H, H] the height of the center of the particle, H = H p -a the effective channel height available to the particle, and X t the position of the center of the particle along the channel. The second and fourth cumulants

⟨X 2 t ⟩ c ≡ ⟨X 2 t ⟩, ⟨X 4 t ⟩ c ≡ ⟨X 4 t ⟩ -3⟨X 2 t ⟩ 2 , (3)
characterize the transport properties of the particle.

Here, ⟨•⟩ denotes the ensemble average, and the initial condition is X t=0 = 0, while Z t=0 follows the equilibrium distribution p 0 . Note that ⟨X 4 t ⟩ c vanishes if X t is Gaussian, therefore its evaluation is the simplest way to quantify the non-Gaussian nature of the process X t . We also define the related non-Gaussianity parameter

α(t) ≡ ⟨X 4 t ⟩ c /⟨X 2 t ⟩ 2 c
. General theory. The process X t obeys the stochastic differential equation:

dX t = 2D ∥ (Z t )dB x,t , (4)
where the Gaussian increments dB x,t have ⟨dB x,t ⟩ = 0 and ⟨dB 2 x,t ⟩ = dt. In Eq. ( 4), we use the Ito prescription of the stochastic calculus, however D ∥ (Z t ) is independent of X t and so this choice is unimportant. Integrating Eq. ( 4) gives

X t = t 0 2D ∥ (Z τ )dB x,τ . (5)
Squaring this and using the independence of dB x,t and Z t , then taking the average yields

⟨X 2 t ⟩ c ≡ ⟨X 2 t ⟩ = 2t H -H dz D ∥ (z)p 0 (z) = 2 D ∥ 0 t , (6)
where ⟨•⟩ 0 denotes the average with respect to the equilibrium distribution p 0 (z). The MSD is purely linear in time, so that X t is Brownian at all times. Taking the fourth-power of Eq. ( 5) and using Wick's (or Isserlis') theorem [START_REF] Coffey | The Langevin equation: with applications to stochastic problems in physics[END_REF] gives [39]

⟨X 4 t ⟩ c 12 = t 0 ds t 0 ds ′ [⟨D ∥ (Z s )D ∥ (Z s ′ )⟩ -⟨D ∥ ⟩ 2 0 ]. (7)
Here, we draw an analogy with Taylor dispersion, for the dispersion of particles in channels in presence of hydrodynamic flows. We imagine the same process Z t , but consider the convective displacement given along the channel by Y t = t 0 ds u(Z s ), where u(z) is an arbitrary imposed flow field along the channel. The first two cumulants of Y t in this problem are

⟨Y t ⟩ c = ⟨u⟩ 0 t, ⟨Y 2 t ⟩ c = t 0 ds t 0 ds ′ [⟨u(Z s )u(Z s ′ )⟩ -⟨u⟩ 2 0 ]. (8)
Comparing the above expressions with Eqs. ( 6) and [START_REF] Wang | Anomalous yet brownian[END_REF] we see that the second and fourth cumulants of X t are proportional to the average and the variance of Y t in a Taylor dispersion problem with the formal correspondence u(z) = D ∥ (z). Taylor dispersion has been widely studied [START_REF] Barton | On the method of moments for solute dispersion[END_REF][START_REF] Biswas | Taylor dispersion with absorbing boundaries: A stochastic approach[END_REF][START_REF] Vedel | Time-dependent tayloraris dispersion of an initial point concentration[END_REF][START_REF] Li | Near-wall nanovelocimetry based on total internal reflection fluorescence with continuous tracking[END_REF][START_REF] Guérin | Force-induced dispersion in heterogeneous media[END_REF][START_REF] Guérin | Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems[END_REF][START_REF] Vilquin | Time dependence of advection-diffusion coupling for nanoparticle ensembles[END_REF][START_REF] Brenner | Macrotransport Processes[END_REF][START_REF] Mercer | A complete model of shear dispersion in pipes[END_REF][START_REF] Balakotaiah | Dispersion of chemical solutes in chromatographs and reactors[END_REF][START_REF] Marbach | Active control of dispersion within a channel with flow and pulsating walls[END_REF][START_REF] Watt | The accurate dynamic modelling of contaminant dispersion in channels[END_REF][START_REF] Alexandre | Generalized Taylor dispersion for translationally invariant microfluidic systems[END_REF], and we can exploit existing results for the MSD at all times from Ref. [START_REF] Alexandre | Generalized Taylor dispersion for translationally invariant microfluidic systems[END_REF], yielding the explicit expression:

⟨X 4 t ⟩ c = 24 H -H dz H -H dz ′ D ∥ (z)D ∥ (z ′ )p 0 (z ′ ) × λ>0 t λ - 1 -e -λt λ 2 ψ Rλ (z)ψ Lλ (z ′ ) , (9)
where ψ Rλ (z) and ψ Lλ (z) respectively denote the right and left eigenfunctions of H, with eigenvalue λ, and the normalization

H -H dz ψ Lλ (z)ψ Rλ (z) = 1.
In practice, this general expression can be evaluated by numerically computing the eigenfunctions after discretizing the operator H. This formula simplifies at short times into (see SI [39]):

X 4 t c ≃ t→0 12 t 2 D 2 ∥ 0 -D ∥ 2 0 . ( 10
)
We see that the initial non-Gaussianity parameter α(t = 0) is finite and is proportional to the variance of D ∥ (z) with respect to the equilibrium distribution, as in Ref. [START_REF] Chubynsky | Diffusing diffusivity: A model for anomalous, yet brownian, diffusion[END_REF]. The late-time behavior is (see SI [39]) 17) and [START_REF] Lanoiselée | A model of nongaussian diffusion in heterogeneous media[END_REF]. (c) Experimentally-measured second cumulant ⟨X 2 t ⟩c. The solid line corresponds to Eq. ( 6), with ⟨D ∥ ⟩0 = 0.58 D0. The slope triangle indicates an exponent 1. (d) Experimentally-measured (green stars) and numericallysimulated (blue dots) fourth cumulant ⟨X 4 t ⟩c. The red solid line represents the prediction of Eq. ( 9), while the black dashed and dotted lines are its short-time and long-time asymptotics of Eqs. [START_REF] Leptos | Dynamics of enhanced tracer diffusion in suspensions of swimming eukaryotic microorganisms[END_REF] and [START_REF] Guan | Even hard-sphere colloidal suspensions display fickian yet non-gaussian diffusion[END_REF], with no adjustable parameter. The slope triangles indicate exponents 2 and 1. (e) Non-Gaussianity parameter α ≡ ⟨X 4 t ⟩c/⟨X 2 t ⟩ 2 c as a function of time t, computed from the data and theoretical predictions in (c) and (d). The red dashed line shows the predicted ∼ 1/t decay (see SI [39]). (f) PDF in horizontal displacement, at time increment t = 0.01 s, from experiments (green stars) and numerical simulations (blue dots). The Gaussian tail predicted in Eq. (S45) (see SI [39]) is also shown (solid line), as well as a simple Gaussian distribution (dashed line) with the proper mean and variance of the data.

⟨X 4 t ⟩ c ≃ t→+∞ 24 (D 4 t -C 4 ) , (11)
where the explicit expression of C 4 is given in the Sup-plementary Information (SI) [39], and where:

D 4 = J(z)e βV (z) 2 D ⊥ (z) 0 , (12)
with:

J(z) = z -H dz ′ e -βV (z ′ ) D ∥ (z ′ ) -⟨D ∥ ⟩ 0 . (13)
From the above we see that the non-Gaussianity parameter satisfies α(t) ∝ 1/t, for large t. Analytic strong confinement theory. We consider the case of a narrow channel where we approximate the local diffusion coefficients by the quadratic expressions [39, [START_REF] Lau | State-dependent diffusion: Thermodynamic consistency and its path integral formulation[END_REF][START_REF] Avni | Brownian motion of a charged colloid in restricted confinement[END_REF]:

D ⊥ (z) ≈ D ⊥0 1 - z 2 H 2 , D ∥ (z) ≈ D ||0 1 - z 2 H 2 s , (14)
where H s is a characteristic distance that can be considered as a slip-like length if H s > H. The coefficients D ⊥0 and D ||0 depend on the effective channel height H and on the particle radius a. In principle, the no-slip boundary condition must impose that D ∥ (z) is zero at the walls, which would imply that H s = H. However, numerically, D ∥ (z) is found to be quadratic near the channel center and decays rapidly to zero near the walls [39,[START_REF] Avni | Brownian motion of a charged colloid in restricted confinement[END_REF]. Here, Eq. ( 9) can be evaluated by noting that the eigenfunctions are the Legendre polynomials P n (z/H) of degree n, leading to:

⟨X 4 t ⟩ c 24 = 2D 2 ||0 H 6 t 135D ⊥0 H 4 s - D 2 ||0 H 8 1 -e -6D ⊥0 t H 2 405D 2 ⊥0 H 4 s . (15)
In this model, there is only one relaxation time, equal to the time for the particle to diffuse perpendicularly. This result can be generalized to arbitrary D ∥ (z), keeping the same form of D ⊥ , in which case many relaxation times appear (see SI [39]). The non-Gaussianity is such that α(0) = (12H 4 )/(5(3H 2 s -H 2 ) 2 ) and is thus of order one. At short times, if one takes H s = H then α(0) = 3/5.

Experimental system. A polystyrene bead, with radius a = 1.519 ± 0.009 µm diffuses in an aqueous NaCl solution confined between two glass walls. Its trajectory is tracked in three dimensions using Mie holography [START_REF] Lavaud | Stochastic inference of surface-induced effects using brownian motion[END_REF]. Here, H p = 40 µm, so that H p ≫ a. The density mismatch of the particle is chosen such that the particle is visibly localized near the lower wall due to gravity (see Fig. 2(a)). So, the effect of the upper wall is negligible both in terms of hydrodynamic and conservative forces. The bead is submitted to a potential:

βV (z) = B e -H+z l D + B e -H-z l D + z l B . ( 16
)
The first two terms of the right-hand side are the screened electrostatic interactions between the negatively-charged surfaces of the walls and the bead, as given mean-field theory [START_REF] Israelachvili | Intermolecular and surface forces[END_REF], where l D is the Debye length and B is a dimensionless number depending in particular on the wall and bead surface charges. We have used the superposition approximation, valid for gaps large compared to l D so that the two potentials can be simply summed. The third term accounts for gravity: l B = k B T /( 4 3 πa 3 ∆ρg) is the Boltzmann length, with g the gravitational acceleration, and ∆ρ the density mismatch between the polystyrene bead and the solution. Equations ( 2) and ( 16) are used to fit the experimentally measured equilibrium distribution p 0 (z). The agreement is good with B = 5.0 ± 0.3, l D = 88 ± 2 nm and l B = 526 ± 5 nm, as shown in Fig. 2(a). Assuming a perfect sphere, the value of l B gives a density mismatch ∆ρ = 53 kg/m 3 , which is within 5% error of the tabulated value of 50 kg/m 3 .

Moving on to hydrodynamic interactions, D ∥ and D ⊥ are inferred from the experimentally observed trajectories [START_REF] Lavaud | Stochastic inference of surface-induced effects using brownian motion[END_REF]39] and are shown in Fig. 2(b). The results agree with the Stokes-Einstein relations

D i (z) = k B T /[6πaµ i (z)]
, where i ∈ {∥, ⊥} and where µ i are the components of the effective viscosity tensor [START_REF] Brenner | The slow motion of a sphere through a viscous fluid towards a plane surface[END_REF]. The transverse component reads [START_REF] Faxen | Die bewegung einer starren kugel langs der achse eines mit zaher flussigkeit gefullten rohres[END_REF]:

µ ∥ (z) = µ 0 1 - 9 16 ζ + 1 8 ζ 3 - 45 256 ζ 4 - 1 16 ζ 5 -1 , (17)
with ζ = a/(z + H p ), and where µ 0 is the bulk viscosity. The normal component was derived in Ref. [START_REF] Brenner | The slow motion of a sphere through a viscous fluid towards a plane surface[END_REF] as an infinite sum, which can be Padé-approximated to within 1% numerical accuracy by [START_REF] Bevan | Hindered diffusion of col-loidal particles very near to a wall: Revisited[END_REF] µ

⊥ (z) = µ 0 6 (z + H) 2 + 9a (z + H) + 2a 2 6 (z + H) 2 + 2a (z + H) . (18)
These expressions, through the associated diffusion coefficients, are in agreement with the experimental data at room temperature and with µ 0 = 1 mPa.s for water, as shown in Fig. 2(b). Combined with the previouslymentioned equilibrium properties (see Eq. ( 16)), they can thus be used as inputs to compute the theoretical values of the fourth cumulant of X t .

Comparison with theory. Experimentally, the displacements X t are used to estimate ⟨X 2 t ⟩ c and ⟨X 4 t ⟩ c , computed using the method of sliding averages described in SI [39] and leading to Figs. 2(c,d). First, the effective diffusion constant, ⟨D ∥ ⟩ 0 defined in Eq. ( 6), is given numerically by ⟨D ∥ ⟩ 0 = 0.58 D 0 , where D 0 = k B T /(6πaµ 0 ) is the bulk diffusion constant. This is in agreement with the experimental data shown in Fig. 2(c). Secondly, the short-time theoretical prediction in Eq. ( 10) correctly predicts the experimental data for ⟨X 4 t ⟩ c , with no adjustable parameter (see Fig. 2(d)). Lack of data at long times makes it difficult to check the late-time prediction given by Eq. ( 11). This result can however be verified through numerical simulations, as shown in Fig. 2(d), where the simulation details are given in SI [39]. The whole range of experimental and numerical data can be reproduced, up to error bars, by the exact prediction of Eq. ( 9), where the eigenfunctions and eigenvalues of H are computed numerically. We thus have a wellcontrolled experimental system with a MSD that is linear in time, at all times, as well as non-Gaussian statistics.

Distribution of displacements. We now study the PDF p(x, t) of the displacement x at time t, in order to determine in particular whether or not it displays apparent exponential tails, as often observed in BNGD [START_REF] Wang | Anomalous yet brownian[END_REF][START_REF] Wang | When brownian diffusion is not gaussian[END_REF][START_REF] Chakraborty | Disorder-induced fickian, yet non-gaussian diffusion in heterogeneous media[END_REF][START_REF] Chechkin | Brownian yet non-gaussian diffusion: from superstatis-tics to subordination of diffusing diffusivities[END_REF][START_REF] Miotto | Length scales in brownian yet non-gaussian dynamics[END_REF][START_REF] Chaudhuri | Universal nature of particle displacements close to glass and jamming transitions[END_REF][START_REF] Rusciano | Fickian Non-Gaussian Diffusion in Glass-Forming Liquids[END_REF][START_REF] Xue | Probing non-Gaussianity in confined diffusion of nanoparticles[END_REF][START_REF] Xue | Diffusion of nanoparticles with activated hopping in crowded polymer solutions[END_REF][START_REF] Pastore | Rapid Fickian yet non-Gaussian diffusion after subdiffusion[END_REF] and other contexts [START_REF] Silva | Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact[END_REF]. We consider a class of systems bounded in the z direction, with a single maximum in D || (z), as is the case in our simulations, experiments and the simple channel model. First, at short times, it is well known [START_REF] Chubynsky | Diffusing diffusivity: A model for anomalous, yet brownian, diffusion[END_REF][START_REF] Chechkin | Brownian yet non-gaussian diffusion: from superstatis-tics to subordination of diffusing diffusivities[END_REF][START_REF] Han | Brownian motion of an ellipsoid[END_REF][START_REF] Lavaud | Stochastic inference of surface-induced effects using brownian motion[END_REF] that

p(x, t) ≃ H -H dz p 0 (z) e -x 2 /[4D ∥ (z)t] 4πD ∥ (z)t . ( 19
)
An analysis of this expression shows that, for large x, one has p(x, t) ≃ Ae -x 2 /4D || (z * )t , where z * is the point where D || (z) is maximal. In SI [39], we compute A, and we show in Fig. 2(f) that such a Gaussian tail is quantitatively recovered in the numerical simulations and experiments. At late times, the PDF can be analysed using its moment-generating function g(q, t) = ⟨e qXt ⟩, which reads: g(q, t) = e q t 0 dBx,s

√ 2D ∥ (Zs) = e q 2 t 0 dsD ∥ (Zs) , (20)
where the last equality is obtained by averaging over the Gaussian noise dB x,s . Interestingly, g(q, t) = ⟨e q 2 Yt ⟩ is related to the moment-generating function for the abovementioned Taylor dispersion problem. We can thus use the tools introduced in the context of Taylor dispersion [START_REF] Haynes | Dispersion in the largedeviation regime. part 2. cellular flow at large péclet num-ber[END_REF][START_REF] Haynes | Dispersion in the largedeviation regime. part 1: shear flows and periodic flows[END_REF][START_REF] Kahlen | Large deviations in taylor dispersion[END_REF] to obtain the extreme tails of p(x, t) at long times, with p(x, t) ∼ e -tf (x/t) . By extreme tails, we mean that ξ = x/t is O(1), thus far from the diffusive scaling limit at late times where x/ √ t is O(1). In SI [39], we show that for large ξ,

f (ξ) = 1 4D || (z * )   ξ + sgn(ξ) |D ′′ || (z * )|D ⊥ (z * ) 2   2 . (21)
The paths contributing to f (ξ) in this regime stay close to the region of maximal diffusivity, but they are rare and are exponentially suppressed with respect to paths which scale diffusively. The presence of Gaussian tails is thus generic for the class of problems studied here, and the exponential tails seen in other diffusing-diffusivity models [START_REF] Chubynsky | Diffusing diffusivity: A model for anomalous, yet brownian, diffusion[END_REF] are absent. The fact that D ∥ (z) has a maximal value is the main difference between our system and those considered in Ref. [START_REF] Chubynsky | Diffusing diffusivity: A model for anomalous, yet brownian, diffusion[END_REF], where the diffusion constant is unbounded. In fact, it was already noted in Ref. [START_REF] Chubynsky | Diffusing diffusivity: A model for anomalous, yet brownian, diffusion[END_REF] that the PDF tails are generally not strictly exponential, depending on the local diffusivity distribution. The Gaussian tails in our system contrast with the case of Continuous Time Random Walks [START_REF] Barkai | Packets of diffusing particles exhibit universal exponential tails[END_REF], and diffusion in confined disordered media [START_REF] Chakraborty | Disorder-induced fickian, yet non-gaussian diffusion in heterogeneous media[END_REF][START_REF] Xue | Probing non-Gaussianity in confined diffusion of nanoparticles[END_REF][START_REF] Xue | Diffusion of nanoparticles with activated hopping in crowded polymer solutions[END_REF] or glassy [START_REF] Chaudhuri | Universal nature of particle displacements close to glass and jamming transitions[END_REF][START_REF] Rusciano | Fickian Non-Gaussian Diffusion in Glass-Forming Liquids[END_REF] systems, where exponentials tails are present. These situations tend to involve trapping, hoping or caging mechanisms (possibly due to heterogeneities) which are absent in our system.

The late-time corrections to Gaussianity in the diffusive-scaling region are dominated by the fourthorder cumulant, which gives a correction to the PDF that decays as ∼ 1/t (see SI [39]). Finally, replacing q = -ik in Eq. ( 20) gives the Fourier transform p(k, t) = ∞ -∞ dx e -ikx p(x, t). This can be computed numerically (see SI [39]). Taking the inverse Fourier transform gives a numerical evaluation of p(x, t) in good agreement with the numerical and experimental PDFs (see Fig. S2 in SI [39]). We have also examined the case where the channel width is much smaller (H p = 5.5 µm). Similar effects are seen, but the asymptotic regime of linear temporal growth of the fourth cumulant is attained much more quickly.

Conclusion. We have addressed a physical realization of diffusing-diffusivity motion based on confined colloids by establishing a mapping onto Taylor dispersion, where the diffusivity formally corresponds to a flow field. This analogy gives quantitative predictions for the diffusion along the channel, which agree with experimental and numerical data with no additional fitting parameter apart from the physical ones obtained independently in the experiments. We have also shown that the tails of the PDF are not exponential but modified Gaussian in this generic class of models, both at short and long times. One should note that the effective diffusion constant along the channel only depends on the equilibrium properties of the process normal to the wall, and is otherwise independent of its dynamics. The fourth cumulant however depends on the precise details of the dynamics via the two-point probability density functions. The fourth cumulant thus carries extra information on the dynamics, and, as such, appears to be a key statistical observable that can further contribute to improve the experimental resolution for the inference of force maps and local transport properties in heterogeneous environments [START_REF] Serov | Statistical tests for force inference in heterogeneous environments[END_REF][START_REF] Frishman | Learning force fields from stochastic trajectories[END_REF] and near surfaces [START_REF] Lavaud | Stochastic inference of surface-induced effects using brownian motion[END_REF].

FIG. 1 .

 1 FIG.1. Schematic: a particle of radius a diffuses in two dimensions, between two walls separated by a distance 2Hp.

2 p

 2 FIG. 2. (a)Experimental long-time PDF p0 for position z, as a function of the distance H + z to the bottom wall. Solid lines show the best fit to the Gibbs-Boltzmann distribution of Eq. (2), using V (z) in Eq. (16), with B = 5.0, lD = 88 nm and lB = 526 nm at room temperature. Here, Hp = 40 µm. Error bars give 95% confidence intervals. (b) Experimentally-measured horizontal (i =∥) and vertical (i =⊥) local diffusion coefficients Di(z), normalized by the bulk value D0. Solid lines are theoretical predictions Di(z) using Eqs. (17) and[START_REF] Lanoiselée | A model of nongaussian diffusion in heterogeneous media[END_REF]. (c) Experimentally-measured second cumulant ⟨X 2 t ⟩c. The solid line corresponds to Eq. (6), with ⟨D ∥ ⟩0 = 0.58 D0. The slope triangle indicates an exponent 1. (d) Experimentally-measured (green stars) and numericallysimulated (blue dots) fourth cumulant ⟨X4 t ⟩c. The red solid line represents the prediction of Eq. (9), while the black dashed and dotted lines are its short-time and long-time asymptotics of Eqs. (10) and[START_REF] Guan | Even hard-sphere colloidal suspensions display fickian yet non-gaussian diffusion[END_REF], with no adjustable parameter. The slope triangles indicate exponents 2 and 1. (e) Non-Gaussianity parameter α ≡ ⟨X 4 t ⟩c/⟨X 2 t ⟩ 2 c as a function of time t, computed from the data and theoretical predictions in (c) and (d). The red dashed line shows the predicted ∼ 1/t decay (see SI[39]). (f) PDF in horizontal displacement, at time increment t = 0.01 s, from experiments (green stars) and numerical simulations (blue dots). The Gaussian tail predicted in Eq. (S45) (see SI[39]) is also shown (solid line), as well as a simple Gaussian distribution (dashed line) with the proper mean and variance of the data.

Acknowledgments:The authors thank Joshua McGraw and Maxence Arutkin for interesting discussions. They acknowledge financial support from the European Union through the European Research Council under EMet-Brown (ERC-CoG-101039103) grant. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. The authors also acknowledge financial sup-port from the Agence Nationale de la Recherche under EMetBrown (ANR-21-ERCC-0010-01), Softer (ANR-21-CE06-0029), Fricolas (ANR-21-CE06-0039), and Com-plexEncounters (ANR-21-CE30-0020) grants. Finally, they thank the Soft Matter Collaborative Research Unit, Frontier Research Center for Advanced Material and Life Science, Faculty of Advanced Life Science at Hokkaido University, Sapporo, Japan.


J Etourneau

J Portier

F Ménil

The role of the inductive effect in solid state chemistry: how the chemist can use it to modify both the structural and the physical properties of the materials

The role of the inductive effect in solid state chemistry: how the chemist can use it to modify both the structural and the physical properties of the materials

Jean Etourneau, Josik Portier, Francis

P a g e | 2 P a g e | 3 P a g e | 4 P a g e | 5 P a g e | 6 P a g e | 7