{"id":1135,"date":"2013-10-29T16:47:43","date_gmt":"2013-10-29T16:47:43","guid":{"rendered":"http:\/\/lptms.u-psud.fr\/christophe_texier\/?page_id=1135"},"modified":"2023-09-04T14:27:48","modified_gmt":"2023-09-04T14:27:48","slug":"interface-model-edwards-wilkinson","status":"publish","type":"page","link":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/recherche\/interface-model-edwards-wilkinson\/","title":{"rendered":"Interface models, elastic lines"},"content":{"rendered":"<h3>Transient dynamics in the Edwards-Wilkinson model<\/h3>\n<p>We study the Langevin dynamics of an interface within the Edwards-Wilkinson model (or equivalently\u00a0 the Rouse chain model for a polymer). We develope a functional Fokker-Planck approach in order to study the effect of pinning of a single monomer and the effect of killing of the monomer (absorption).<\/p>\n<p style=\"padding-left: 180px;\"><a href=\"\/christophe_texier\/files\/2013\/10\/pinned-edwards-wilkinson.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1631\" src=\"\/christophe_texier\/files\/2013\/10\/pinned-edwards-wilkinson-300x123.png\" alt=\"pinned-edwards-wilkinson\" width=\"300\" height=\"123\" srcset=\"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/files\/2013\/10\/pinned-edwards-wilkinson-300x123.png 300w, http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/files\/2013\/10\/pinned-edwards-wilkinson.png 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<ul>\n<li>Shamik Gupta, Alberto Rosso and Christophe Texier,<br \/>\n<strong>Dynamics of a tagged monomer: Effects of elastic pinning and harmonic absorption<\/strong><br \/>\n<a href=\"http:\/\/prl.aps.org\/abstract\/PRL\/v111\/i21\/e210601\"> Phys. Rev. Lett. <strong>111<\/strong>, 210601 (2013)<\/a><br \/>\n<a href=\"http:\/\/arxiv.org\/abs\/1308.0284\">cond-mat arXiv:1308.0284.<\/a><\/li>\n<\/ul>\n<h3>Distribution of the center of mass of interfaces<\/h3>\n<p>We consider a model of Brownian <em>N<\/em> non intersecting interfaces with a repulsive substrate. Nadal &amp; Majumdar [<a href=\"http:\/\/journals.aps.org\/pre\/abstract\/10.1103\/PhysRevE.79.061117\">Phys. Rev. E <strong>79<\/strong>, 061117 (2009)<\/a>] have studied the distribution of the position of the highest interface, <em>h<\/em><sub>1<\/sub>, and also the distribution of the center of mass <em>G<\/em>=(1\/<em>N<\/em>)\u03a3<em><sub>i<\/sub><\/em><sub>=1<\/sub><sup><em>N<\/em><\/sup> <em>h<sub>i<\/sub><\/em>.<\/p>\n<p style=\"padding-left: 150px;\"><a href=\"\/christophe_texier\/files\/2013\/10\/Schema_interf.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1630\" src=\"\/christophe_texier\/files\/2013\/10\/Schema_interf-300x225.png\" alt=\"schema_interf\" width=\"300\" height=\"225\" srcset=\"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/files\/2013\/10\/Schema_interf-300x225.png 300w, http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/files\/2013\/10\/Schema_interf-1024x768.png 1024w, http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/files\/2013\/10\/Schema_interf.png 1333w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>In this article we consider the distribution of the fraction \u03ba=<em>N<\/em><sub>1<\/sub>\/<em>N<\/em> of top interfaces. Using a mapping on a random matrix problem (within the Laguerre ensemble) we are led to study the distribution of a truncated linear statistics of the eigenvalues of Wishart matrices.<\/p>\n<ul>\n<li>Aur\u00e9lien Grabsch, Satya N. Majumdar and Christophe Texier,<br \/>\n<strong> Truncated linear statistics associated with the top eigenvalues of random matrices ,<br \/>\n<\/strong><a href=\"http:\/\/link.springer.com\/article\/10.1007\/s10955-017-1755-5?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst\">J. Stat. Phys. <strong>167<\/strong>(2), 234-259 (2017)<\/a><br \/>\n<a href=\"http:\/\/arxiv.org\/abs\/1609.08296\">cond-mat arXiv:1609.08296<\/a><\/li>\n<\/ul>\n<p style=\"padding-left: 60px;\"><span style=\"color: #ff0000;\"><strong>See also<span style=\"color: #000000;\"> page \u00a0\u201c <a href=\"\/christophe_texier\/recherche\/random-matrix-theory\/invariant-ensembles-linear-statistics-of-the-eigenvalues-and-coulomb-gas\/\">Random matrix theory<\/a> \u201d<br \/>\n<\/span><\/strong><\/span><\/p>\n<h3>Counting equilibria for a directed polymer in a random environment<\/h3>\n<p>At <em>T<\/em>=0, an elastic line in a disordered medium submitted to a uniform force field is pinned by the disorder for a force below a critical threshold f<sub>c<\/sub>. We consider this problem by studying the average number of equilibria (stable or unstable).<\/p>\n<p style=\"padding-left: 210px;\"><a href=\"\/christophe_texier\/files\/2013\/10\/niceline-big.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1776\" src=\"\/christophe_texier\/files\/2013\/10\/niceline-big-200x300.png\" alt=\"niceline-big\" width=\"147\" height=\"221\" srcset=\"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/files\/2013\/10\/niceline-big-200x300.png 200w, http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/files\/2013\/10\/niceline-big.png 299w\" sizes=\"auto, (max-width: 147px) 100vw, 147px\" \/><\/a><\/p>\n<p>We establish an interesting connection between the counting problem and the Anderson localisation of wave by a random potential.<\/p>\n<ul>\n<li>Yan V. Fyodorov, Pierre Le Doussal, Alberto Rosso and Christophe Texier,<br \/>\n<strong>Exponential number of equilibria and depinning threshold for a directed polymer in a random potential<\/strong>,<br \/>\n<a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0003491618302008?via%3Dihub\">Ann. Phys. <strong>397<\/strong>, p. 1-64 (2018)<\/a><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/1703.10066\">cond-mat.dis-nn arXiv:1703.10066<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Transient dynamics in the Edwards-Wilkinson model We study the Langevin dynamics of an interface within the Edwards-Wilkinson model (or equivalently\u00a0 the Rouse chain model for a polymer). We develope a functional Fokker-Planck approach in order to study the effect of &hellip; <a href=\"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/recherche\/interface-model-edwards-wilkinson\/\">Continuer la lecture <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"parent":36,"menu_order":25,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1135","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/1135","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/comments?post=1135"}],"version-history":[{"count":25,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/1135\/revisions"}],"predecessor-version":[{"id":2713,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/1135\/revisions\/2713"}],"up":[{"embeddable":true,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/36"}],"wp:attachment":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/media?parent=1135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}