{"id":461,"date":"2022-02-21T15:07:09","date_gmt":"2022-02-21T23:07:09","guid":{"rendered":"\/wp\/hades\/?p=461"},"modified":"2022-02-21T15:07:09","modified_gmt":"2022-02-21T23:07:09","slug":"dynamics-of-a-maximally-open-quantized-cat-map","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2022\/02\/21\/dynamics-of-a-maximally-open-quantized-cat-map\/","title":{"rendered":"Dynamics of a Maximally Open Quantized Cat Map"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday,\u00a0<strong>February 22<\/strong> will be at <strong>3:30 pm<\/strong> in <strong>Room 740<\/strong>.<\/p>\n\n\n\n<p><strong>Speaker<\/strong>: Yonah Borns-Weil<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: Quantum dynamics is concerned with quantum analogues of classical dynamical systems. A common situation is\u00a0scattering\u00a0theory, in which the Hamiltonian dynamics of scattered particles are replaced by wavefunctions\u00a0obeying the Schr\u00f6dinger equation. When time is discretized, the analogues are\u00a0<em>open quantum maps<\/em>, which are Fourier integral operators arising from phase space diffeomorphisms that are then &#8220;opened&#8221; by sending some regions to &#8220;infinity.&#8221; In this talk, we analyze a simple open quantum map, based on the classical Arnol&#8217;d cat map. We shall show using the method of Grushin problems that the spectrum has a very simple form in the semiclassical regime as h approaches 0. Emphasis will be given to motivation and interpretations of the result.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0February 22 will be at 3:30 pm in Room 740. Speaker: Yonah Borns-Weil Abstract: Quantum dynamics is concerned with quantum analogues of classical dynamical systems. A common situation is\u00a0scattering\u00a0theory, in which the Hamiltonian dynamics of scattered particles are replaced by wavefunctions\u00a0obeying the Schr\u00f6dinger equation. When time is discretized, the analogues are\u00a0open [&hellip;]<\/p>\n","protected":false},"author":91,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-461","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/461","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\/91"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=461"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/461\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=461"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=461"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=461"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}