{"id":1192,"date":"2024-12-01T14:20:32","date_gmt":"2024-12-01T22:20:32","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1192"},"modified":"2025-01-21T11:09:41","modified_gmt":"2025-01-21T19:09:41","slug":"characterizing-the-support-of-semiclassical-measures-for-quantum-cat-maps","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2024\/12\/01\/characterizing-the-support-of-semiclassical-measures-for-quantum-cat-maps\/","title":{"rendered":"Characterizing the support of semiclassical measures for quantum cat maps"},"content":{"rendered":"<p>The HADES seminar on Tuesday, <strong>December<\/strong><strong>\u00a03rd<\/strong>, will be at\u00a0<strong>2<\/strong><strong>:00pm<\/strong>\u00a0in\u00a0<strong>Room 740.<\/strong><\/p>\n<p><strong>Speaker:\u00a0<\/strong>Elena Kim<\/p>\n<p><strong>Abstract: <\/strong>We consider a quantum cat map $M$ associated to a symplectic matrix $A$ acting on the torus $\\mathbb{T}^{2n}$, a popular model in quantum chaos. The semiclassical limit of the mass of eigenfunctions of $M$ is characterized by the semiclassical measure.<\/p>\n<p>For the analogous model on hyperbolic manifolds, the quantum unique ergodicity conjecture posits that the Liouville measure is the only semiclassical measure; however, the corresponding statement for quantum cat maps is known to be false. It is thus an open question to otherwise describe semiclassical measures for quantum cat maps.<\/p>\n<p>In this talk, I will explain how the higher-dimensional fractal uncertainty principle of Cohen can be used to characterize the supports of semiclassical measures $\\mu$, including cases where $\\mu$ has full support.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, December\u00a03rd, will be at\u00a02:00pm\u00a0in\u00a0Room 740. Speaker:\u00a0Elena Kim Abstract: We consider a quantum cat map $M$ associated to a symplectic matrix $A$ acting on the torus $\\mathbb{T}^{2n}$, a popular model in quantum chaos. The semiclassical limit of the mass of eigenfunctions of $M$ is characterized by the semiclassical measure. For the [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[],"class_list":["post-1192","post","type-post","status-publish","format-standard","hentry","category-fall-2024"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1192","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1192"}],"version-history":[{"count":2,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1192\/revisions"}],"predecessor-version":[{"id":1195,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1192\/revisions\/1195"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}