A Gutzwiller trace formula for large hermitian matrices

Jens Bolte, Sebastian Egger, Stefan Keppeler

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Abstract

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 Schrödinger equation. In the framework of Weyl quantization, 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 quantization condition for eigenvalues as well as some simple examples.
Original languageEnglish
JournalReviews in Mathematical Physics
Volume29
Issue number8
Early online date10 Aug 2017
DOIs
Publication statusPublished - 2017

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