A Gutzwiller trace formula for large hermitian matrices

We develop a semiclassical approximation for the dynamics of quantum systems in finite-dimensional Hilbert spaces whose classical counterparts are defined on a toroidal phase space. In contrast to previous models of quantum maps, the time evolution is in continuous time and, hence, is generated by a...

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Bibliographic Details
Published inarXiv.org
Main Authors Bolte, Jens, Egger, Sebastian, Keppeler, Stefan
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.08.2017
Subjects
Eigenvalues
Evolution
Hilbert space
Mathematics - Mathematical Physics
Operators (mathematics)
Physics - Chaotic Dynamics
Physics - Mathematical Physics
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Summary:We develop a semiclassical approximation for the dynamics of quantum systems in finite-dimensional Hilbert spaces whose classical counterparts are defined on a toroidal phase space. In contrast to previous models of quantum maps, the time evolution is in continuous time and, hence, is generated by a Schr\"odinger equation. In the framework of Weyl quantisation, we construct discrete, semiclassical Fourier integral operators approximating the unitary time evolution and use these to prove a Gutzwiller trace formula. We briefly discuss a semiclassical quantisation condition for eigenvalues as well as some simple examples.
ISSN:2331-8422
DOI:10.48550/arxiv.1512.05984