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arXiv · 1512.05984

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 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.

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Jens Bolte, Sebastian Egger, Stefan Keppeler. 2017-08-03. A Gutzwiller trace formula for large hermitian matrices. https://doi.org/10.1142/s0129055x17500271

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