{"id":2280,"date":"2020-01-07T23:17:50","date_gmt":"2020-01-07T23:17:50","guid":{"rendered":"http:\/\/lptms.u-psud.fr\/christophe_texier\/?page_id=2280"},"modified":"2023-09-04T14:26:49","modified_gmt":"2023-09-04T14:26:49","slug":"ordered-statistics-of-energy-levels","status":"publish","type":"page","link":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/recherche\/some-properties-of-the-one-dimensional-schrodinger-operator-with-random-potential\/ordered-statistics-of-energy-levels\/","title":{"rendered":"Ordered statistics of energy levels"},"content":{"rendered":"<h3>Ordered (extreme value) statistics of energy levels for 1D disordered quantum mechanics<\/h3>\n<ul>\n<li>Christophe Texier,<br \/>\n<strong>Individual energy level distributions for one-dimensional diagonal and off-diagonal disorder<\/strong><br \/>\n<a href=\"http:\/\/iopscience.iop.org\/0305-4470\/33\/35\/303\">J. Phys. A: Math. Gen. <strong>33<\/strong>, 6095-6128 (2000).<\/a><br \/>\n<a href=\"http:\/\/xxx.lanl.gov\/abs\/cond-mat\/0004285\">cond-mat\/0004285.<\/a><\/li>\n<\/ul>\n<p>Dirac equation with a random mass is known to support a critical extended state at zero energy (note that Dirac operator is directly related to the <a href=\"\/christophe_texier\/recherche\/a-review-article\/\">supersymmetric Schr\u00f6dinger Hamiltonian<\/a>). We analyse the average density of states for 1D Dirac operator in a bounded domain. Due to delocalisation, the DoS is sensitive to the boundaries for <em>E<\/em> \u2192 0. This provides a possible definition of the localisation length, much larger than the inverse localisation length, that usually provides a definition of localisation in 1D problems. We argue that Lyapunov exponent is not able to capture the essential physics of low energy localisation near the delocalisation point (<em>E<\/em>=0).<\/p>\n<ul>\n<li>Christophe Texier and Christian Hagendorf,<br \/>\n<strong>Effect of boundaries on the spectrum of a one-dimensional random mass Dirac Hamiltonian<\/strong><br \/>\n<a href=\"iopscience.iop.org\/1751-8121\/43\/2\/025002\">J. Phys. A: Math. Theor. <strong>43<\/strong>, 025002 (2010).<\/a> (12pp)<br \/>\n<a href=\"http:\/\/arxiv.org\/abs\/0909.2205\">cond-mat arXiv:0909.2205.<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Ordered (extreme value) statistics of energy levels for 1D disordered quantum mechanics Christophe Texier, Individual energy level distributions for one-dimensional diagonal and off-diagonal disorder J. Phys. A: Math. Gen. 33, 6095-6128 (2000). cond-mat\/0004285. Dirac equation with a random mass is &hellip; <a href=\"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/recherche\/some-properties-of-the-one-dimensional-schrodinger-operator-with-random-potential\/ordered-statistics-of-energy-levels\/\">Continuer la lecture <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"parent":42,"menu_order":12,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2280","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/2280","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=2280"}],"version-history":[{"count":2,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/2280\/revisions"}],"predecessor-version":[{"id":2712,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/2280\/revisions\/2712"}],"up":[{"embeddable":true,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/42"}],"wp:attachment":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/media?parent=2280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}