A Gutzwiller trace formula for large hermitian matrices
arXiv:1512.05984 · doi:10.1142/S0129055X17500271
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.
41 pages; extended introduction; added appendix an comparison of anti-Wick and Weyl quantisation