{"id":587,"date":"2025-02-15T00:55:35","date_gmt":"2025-02-15T00:55:35","guid":{"rendered":"https:\/\/pages.charlotte.edu\/probability-seminar\/?p=587"},"modified":"2025-02-16T03:55:52","modified_gmt":"2025-02-16T03:55:52","slug":"wed-feb-12-2024-at-200pm-in-fretwell-379-math-conference-room","status":"publish","type":"post","link":"https:\/\/pages.charlotte.edu\/probability-seminar\/blog\/2025\/02\/15\/wed-feb-12-2024-at-200pm-in-fretwell-379-math-conference-room\/","title":{"rendered":"Wed Feb 12, 2025 at 2:00PM in Fretwell 379 (Math Conference Room)"},"content":{"rendered":"\n<p><a href=\"https:\/\/math.charlotte.edu\/directory\/oleg-safronov\">Oleg Safronov<\/a>, UNC Charlotte<\/p>\n\n\n\n<p>Title: Localization on quantum graphs.<\/p>\n\n\n\n<p>Abstract: I would give some basic definitions\u00a0 that\u00a0 are needed to understand what a localization is. One\u00a0 needs to define such notions as pure point\u00a0 spectrum and how\u00a0could it\u00a0be dense in some intervals. The localization will\u00a0 be discussed for\u00a0 the\u00a0\u00a0<strong>random\u00a0<\/strong>Schrodinger operator\u00a0 on the graph\u00a0defined\u00a0 as\u00a0 the union of intervals of length 1 connecting\u00a0 points\u00a0 of the lattice Z^d. The vertices\u00a0of this graph are\u00a0 called &#8220;junctions&#8221;. Randomness of\u00a0 properties \u00a0of\u00a0 &#8220;junctions&#8221; will cause\u00a0 the particles or waves with certain energies\u00a0 to localize\u00a0 (i.e. to be trapped) in the corresponding medium.\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Oleg Safronov, UNC Charlotte Title: Localization on quantum graphs. Abstract: I would give some basic definitions\u00a0 that\u00a0 are needed to understand what a localization is. One\u00a0 needs to define such notions as pure point\u00a0 spectrum and how\u00a0could it\u00a0be dense in some intervals. The localization will\u00a0 be discussed for\u00a0 the\u00a0\u00a0random\u00a0Schrodinger operator\u00a0 on the graph\u00a0defined\u00a0 as\u00a0 the [&hellip;]<\/p>\n","protected":false},"author":16,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-587","post","type-post","status-publish","format-standard","hentry","category-probability_seminar"],"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts\/587","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/comments?post=587"}],"version-history":[{"count":2,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts\/587\/revisions"}],"predecessor-version":[{"id":589,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts\/587\/revisions\/589"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/media?parent=587"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/categories?post=587"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/tags?post=587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}