{"id":1186,"date":"2014-03-27T11:59:05","date_gmt":"2014-03-27T11:59:05","guid":{"rendered":"http:\/\/lptms.u-psud.fr\/christophe_texier\/?page_id=1186"},"modified":"2025-03-12T21:51:47","modified_gmt":"2025-03-12T21:51:47","slug":"onde-en-milieu-desordonne","status":"publish","type":"page","link":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/enseignements\/enseignements-en-master\/onde-en-milieu-desordonne\/","title":{"rendered":"M2 iCFP &#8211; Ondes en milieux d\u00e9sordonn\u00e9s et ph\u00e9nom\u00e8nes de localisation"},"content":{"rendered":"<h1 style=\"text-align: center\"><span style=\"color: #0000ff\"><strong>Waves in disordered media and localisation phenomena<br \/>\n<\/strong><\/span><\/h1>\n<p style=\"text-align: center\"><a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/0370157384901030\"><img loading=\"lazy\" decoding=\"async\" src=\"\/christophe_texier\/files\/2014\/03\/bergmannPhysRep_fig2-10.jpg\" alt=\"\" width=\"250\" height=\"174\" \/><\/a><a href=\"http:\/\/iopscience.iop.org\/0295-5075\/21\/5\/008\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"\/christophe_texier\/files\/2014\/03\/erbacher_epl21_fig4.jpg\" alt=\"\" width=\"169\" height=\"174\" \/><\/a><\/p>\n<h3><a href=\"http:\/\/enseignement.phys.ens.fr\/spip.php?rubrique284\">Master iCFP<\/a>, <a href=\"http:\/\/enseignement.phys.ens.fr\/spip.php?rubrique287\">Quantum physics<\/a><\/h3>\n<p style=\"padding-left: 30px\">2013-2021 : Course &amp; Exercices<\/p>\n<p>Lectures given in collaboration with <a href=\"http:\/\/www.lkb.upmc.fr\/complexquantumsystems\/nicolas-cherroret\/\">Nicolas Cherroret<\/a> from\u00a0 <a href=\"http:\/\/www.spectro.jussieu.fr\/\">Laboratoire Kastler-Brossel<\/a>, UPMC, Jussieu (and, from 2013 to 2016 with <a href=\"http:\/\/www.lkb.upmc.fr\/complexquantumsystems\/dominique-delande\/\">Dominique Delande<\/a>)<\/p>\n<p style=\"padding-left: 30px\">\u21d2 <strong>Lecture notes<\/strong> (<span style=\"color: #008000\">updated: 04\/02\/2021<\/span>)<\/p>\n<h3>Program (10 lectures) :<\/h3>\n<h4 style=\"padding-left: 30px\">1. Introduction : disorder is everywhere (NC)<\/h4>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/03\/td1_bloch_oscillations.pdf\">Bloch oscillations<\/a> (DD)<\/p>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/03\/td1wrm-Nicolas-Cherroret-01-2018.pdf\">Wave diffusion through a slice of disordered medium<\/a> (NC)<\/p>\n<h4 style=\"padding-left: 30px\">2. Anderson localisation in one dimension (CT)<\/h4>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/03\/td2wrm.pdf\">Thouless relation<\/a> (CT)<\/p>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/03\/td3wrm.pdf\">Localisation and Lishits tail in the Frisch-Lloyd model<\/a> (CT)<\/p>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2019\/01\/td2ter-wrm.pdf\">The Landauer approach and the distribution of the conductance<\/a> (CT)<\/p>\n<h4 style=\"padding-left: 30px\">3. Scaling theory (NC)<\/h4>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/03\/td3bis-wrm.pdf\">The scaling approach of 1D localisation &#8212; distribution of the transmission probability<\/a> (CT)<\/p>\n<p style=\"padding-left: 60px\">TD :\u00a0<a href=\"\/christophe_texier\/files\/2014\/03\/td3wrm-Nicolas-Cherroret-01-2018.pdf\">Ioffe-Regel criterion: matter waves versus electromagnetic waves<\/a> (NC)<\/p>\n<h4 style=\"padding-left: 30px\">\u00a04 to 6. Quantum transport in weakly disordered metals (CT)<\/h4>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/04\/td4wrm.pdf\">Classical and anomalous magneto-conductance<\/a> (CT)<\/p>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/04\/td5wrm.pdf\">Magneto-conductance of 2D metals<\/a> (CT)<\/p>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/03\/td5bis-wrm.pdf\">Spin-orbit scattering and weak anti-localisation in metallic films<\/a> (CT)<\/p>\n<h4 style=\"padding-left: 30px\">7. Universal conductance fluctuations (CT)<\/h4>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/03\/td7wrm.pdf\">Conductance fluctuations and correlations in narrow wires<\/a> (CT)<\/p>\n<h4 style=\"padding-left: 30px\">8. Coherent back-scattering (NC)<\/h4>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/03\/td6wrm_CBS.pdf\">Shape of the coherent back-scattering peak<\/a> (DD)<\/p>\n<h4 style=\"padding-left: 30px\">9. Self-consistent theory of localisation (NC)<\/h4>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/05\/td8wrm_kicked_rotor.pdf\">Kicked rotor<\/a> (DD)<\/p>\n<h4 style=\"padding-left: 30px\">10. Dephasing and decoherence (NC)<\/h4>\n<h4 style=\"padding-left: 60px\">\u00a0(Interaction effects, CT)<\/h4>\n<p style=\"padding-left: 60px\">TD : <a href=\"\/christophe_texier\/files\/2014\/03\/td9wrm.pdf\">Decoherence by electronic interactions &#8212; Influence functional approach<\/a> (CT)<\/p>\n<h3>Exams\u00a0 :<\/h3>\n<ul>\n<li>11 june 2014 :<!-- href=\"\/christophe_texier\/files\/2014\/03\/wrm_exam1406.pdf\"--> Aharonov-Bohm and Altshuler-Aronov-Spivak oscillations in rings and hollow cylinders<\/li>\n<li>10 june 2015 : <!-- href=\"\/christophe_texier\/files\/2014\/03\/wrm_exam1506.pdf\"--> Role of contacts in WL measurements and nonlocality of quantum transport<\/li>\n<li>08 june 2016 : <!-- href=\"\/christophe_texier\/files\/2014\/03\/wrm_exam1606_suj.pdf\"-->Anderson localisation of cold atoms in a disordered speckle potential<\/li>\n<li>29 march 2017 : <a href=\"\/christophe_texier\/files\/2014\/03\/wrm_exam1703_suj.pdf\">Quantum electronic transport in narrow 2D disordered metallic wires<\/a> &#8212; <a href=\"\/christophe_texier\/files\/2014\/03\/wrm_exam1703_corr.pdf\">solutions<\/a><\/li>\n<li>\u00a030 march 2018 : <a href=\"\/christophe_texier\/files\/2018\/03\/wrm_exam1803.pdf\" rel=\"attachment wp-att-1945\">Non-linear conductance of a coherent metallic wire &#8212; Effect of decoherence on CBS and Anderson localisation<\/a> &#8212; <a href=\"\/christophe_texier\/files\/2018\/03\/wrm_exam1803-corr-pb1.pdf\" rel=\"attachment wp-att-1946\">solution pb 1<\/a> &#8212; <a href=\"\/christophe_texier\/files\/2018\/03\/wrm_exam1803-corr-pb2.pdf\" rel=\"attachment wp-att-1947\">solution pb 2<\/a><\/li>\n<li>5 april 2019 : <a href=\"\/christophe_texier\/files\/2019\/04\/wrm_exam1904.pdf\">Metal insulator (Anderson) transition in 2D ?<\/a> &#8211; <a href=\"\/christophe_texier\/files\/2019\/04\/wrm_exam1904-corr.pdf\">solutions<\/a><\/li>\n<li>3 april 2020 : <a href=\"\/christophe_texier\/files\/2020\/04\/wrm_exam2004-sub.pdf\">DoS correction and AA correction &#8211; Self consistent theory of localization in finite media<\/a> &#8211; <a href=\"\/christophe_texier\/files\/2020\/04\/wrm_exam2004-corr-pb1-CT.pdf\">correction of pb1<\/a> &#8211; c<a href=\"\/christophe_texier\/files\/2020\/04\/wrm_exam2004-corr-pb2-NC.pdf\">orrection of pb2<\/a><\/li>\n<li>2 april 2021 : <a href=\"\/christophe_texier\/files\/2021\/04\/wrm_exam2104.pdf\">Magnetoconductance oscillations in a ring &#8212; CBS versus optical coherence<\/a> ; <a href=\"\/christophe_texier\/files\/2021\/04\/wrm_exam2104_corr.pdf\">correction<\/a><\/li>\n<li>8 april 2022 :\u00a0<a href=\"\/christophe_texier\/files\/2022\/04\/wrm_exam2204.pdf\">Weak localization correction in a hollow cylinder &#8212; Speckle correlations and memory effect<\/a> ;\u00a0<a href=\"\/christophe_texier\/files\/2022\/04\/wrm_exam2204-corr.pdf\">correction pb1<\/a><\/li>\n<\/ul>\n<h3>Bibliography :<\/h3>\n<ul>\n<li>A book (emphasize on 1D case and exact results) : J.-M. Luck, \u00ab\u00a0<em>Syst\u00e8mes d\u00e9sordonn\u00e9s unidimensionnels<\/em>\u00ab\u00a0, CEA, collection Al\u00e9a Saclay (1992).<\/li>\n<li>A book (advanced, with emphasize on strong localisation) : I. M. Lifshitz, S. A. Gredeskul &amp; L. A. Pastur, \u00ab\u00a0<em>Introduction to the theory of disordered systems<\/em>\u00ab\u00a0, John Wiley &amp; Sons (1988).<\/li>\n<li>A book (introductory, emphasize on mesoscopic physics, brief introduction to diagrammatic approach) : S. Datta, \u00ab\u00a0<em>Electronic transport in mesoscopic systems<\/em>\u00ab\u00a0, <a href=\"http:\/\/www.cambridge.org\/fr\/academic\/subjects\/engineering\/electronic-optoelectronic-devices-and-nanotechnology\/quantum-transport-atom-transistor?format=PB\">Cambridge University Press (1995)<\/a><\/li>\n<li>A complete and pedagogical presentation (photons and electrons in parallel, emphasize on weak localisation regime) :\u00a0E. Akkermans &amp; G. Montambaux, \u00ab\u00a0<em>Mesoscopic physics of electrons and photons<\/em>\u00ab\u00a0, <a href=\"http:\/\/www.cambridge.org\/fr\/academic\/subjects\/physics\/condensed-matter-physics-nanoscience-and-mesoscopic-physics\/mesoscopic-physics-electrons-and-photons?format=PB\">Cambridge University Press (2007)<\/a> ; in french :<a href=\"http:\/\/www.edition-sciences.com\/physique-mesoscopique-electrons-et-photons.htm\"> EDP Sciences, CNRS \u00e9ditions (2004)<\/a><\/li>\n<li>Introductory articles (weak localisation regime) : B. L. Altshuler &amp; P. A. Lee, \u00ab\u00a0<em>Disordered electronic systems<\/em>\u00ab\u00a0, Physics Today <strong>41<\/strong>, 36-44 (1988) ; R. A. Webb &amp; S. Washburn, \u00ab\u00a0<em>Quantum interference fluctuations in disordered metals<\/em>\u00ab\u00a0, Physics Today <strong>41<\/strong>, 46-53 (1988) ; and, (atomic physics) : L. Sanchez-Palencia and M. Lewenstein, \u00ab\u00a0<em>Disordered quantum gases under control<\/em>\u00ab\u00a0, <a href=\"http:\/\/www.nature.com\/nphys\/journal\/v6\/n2\/abs\/nphys1507.html\">Nature Phys. <strong>6<\/strong>, 87-95 (Feb. 2010).<\/a><\/li>\n<li>Review articles (theory oriented) :\n<ul>\n<li>(pedagogical presentation based on path integral) : S. Chakravarty &amp; A. Schmid, \u00ab\u00a0<em>Weak localization: the quasiclassical theory of electrons in a random potential<\/em>\u00ab\u00a0, <a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/037015738690027X\">Phys. Rep.\u00a0<strong>140<\/strong>, 193-236 (1986)<\/a> ;<\/li>\n<li>(emphasize on scaling theory) B. Kramer &amp; A. MacKinnon, \u00ab\u00a0<a href=\"http:\/\/www.cmth.ph.ic.ac.uk\/people\/a.mackinnon\/Research\/Papers\/rp931201.pdf\"><em>Localization: theory and experiment<\/em><\/a>\u00ab\u00a0, Rep. Prog. Phys. <strong>56<\/strong>, 1469-1564 (1993) ;<\/li>\n<li>(emphasize on interaction effects) P. A. Lee &amp; T. V. Ramakrishnan, \u00ab\u00a0<em>Disordered electronic systems<\/em>\u00ab\u00a0, <a href=\"http:\/\/journals.aps.org\/rmp\/abstract\/10.1103\/RevModPhys.57.287\">Rev. Mod. Phys.\u00a0<strong>57<\/strong>, 287-337 (1985)<\/a> ;<\/li>\n<\/ul>\n<\/li>\n<li>Review articles (experiment oriented) :\n<ul>\n<li>(emphasize on WL in 2D) G. Bergmann, \u00ab\u00a0<a href=\"http:\/\/physics.usc.edu\/~bergmann\/Preprints\/B30.pdf\">Weak localization in thin films<\/a>\u00ab\u00a0, Phys. Rep. <strong>107<\/strong>, 1-58 (1984)<\/li>\n<li>(emphasize on fluctuations and AB oscillations) S. Washburn &amp; R. Webb, \u00ab\u00a0<em>Aharonov-Bohm effect in normal metal. Quantum coherence and transport<\/em>\u00ab\u00a0, <a href=\"http:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/00018738600101921#.U0HRE8foUtU\">Adv. Phys. <strong>35<\/strong>, 375-422 (1986)<\/a><\/li>\n<li>(emphasize on quantum oscillations) A. G. Aronov &amp; Yu. V. Sharvin, \u00ab\u00a0<em>Magnetic flux effects in disordered conductors<\/em>\u00ab\u00a0, <a href=\"http:\/\/journals.aps.org\/rmp\/abstract\/10.1103\/RevModPhys.59.755\">Rev. Mod. Phys. <strong>59<\/strong>, 755 (1987)<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Waves in disordered media and localisation phenomena Master iCFP, Quantum physics 2013-2021 : Course &amp; Exercices Lectures given in collaboration with Nicolas Cherroret from\u00a0 Laboratoire Kastler-Brossel, UPMC, Jussieu (and, from 2013 to 2016 with Dominique Delande) \u21d2 Lecture notes (updated: &hellip; <a href=\"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/enseignements\/enseignements-en-master\/onde-en-milieu-desordonne\/\">Continuer la lecture <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"parent":11,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1186","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/1186","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=1186"}],"version-history":[{"count":105,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/1186\/revisions"}],"predecessor-version":[{"id":3054,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/1186\/revisions\/3054"}],"up":[{"embeddable":true,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/11"}],"wp:attachment":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/media?parent=1186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}