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Arbeitsgemeinschaft: Quantum Ergodicity

dc.date.accessioned2019-10-24T14:23:03Z
dc.date.available2019-10-24T14:23:03Z
dc.date.issued2011
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3264
dc.description.abstractQuantum Ergodicity aims at understanding the eigenstates of quantum mechanical systems admitting chaotic classical limiting dynamics. A paradigmatic system is the Laplace-Beltrami operator on a compact manifold of negative sectional curvature: its classical limit is the geodesic flow on the manifold, which is of Anosov type. Although no explicit expression is available for the eigenstates, one may use various tools from semiclassical analysis in order to gather some partial information on their structure. The central result (Quantum Ergodicity Theorem) states that almost all eigenstates are equidistributed over the energy shell, in the semiclassical limit, provided the classical system is ergodic. The lectures review the background techniques of semiclassical analysis and ergodic theory, give several versions of the QE theorem, and present several extensions of the result, which apply to specific systems, for instance chaotic systems enjoying arithmetic symmetries.
dc.titleArbeitsgemeinschaft: Quantum Ergodicity
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWR-2011-49
local.series.idOWR-2011-49
local.subject.msc81
local.subject.msc35
local.sortindex704
local.date-range09 Oct - 14 Oct 2011
local.workshopcode1141
local.workshoptitleArbeitsgemeinschaft: Quantum Ergodicity
local.organizersUlrich Bunke, Regensburg; Stephane Nonnenmacher, Gif-sur-Yvette; Roman Schubert, Bristol
local.report-nameWorkshop Report 2011,49
local.opc-photo-id1141
local.publishers-doi10.4171/OWR/2011/49
local.ems-referenceBunke Ulrich, Nonnenmacher Stephane, Schubert Roman: Arbeitsgemeinschaft: Quantum Ergodicity. Oberwolfach Rep. 8 (2011), 2781-2835. doi: 10.4171/OWR/2011/49


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