A Gutzwiller trace formula for large hermitian matrices
Mathematical Physics
2017-09-04 v3 math.MP
Chaotic Dynamics
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 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.
Cite
@article{arxiv.1512.05984,
title = {A Gutzwiller trace formula for large hermitian matrices},
author = {Jens Bolte and Sebastian Egger and Stefan Keppeler},
journal= {arXiv preprint arXiv:1512.05984},
year = {2017}
}
Comments
41 pages; extended introduction; added appendix an comparison of anti-Wick and Weyl quantisation