A Gutzwiller trace formula for large hermitian matrices

Jens Bolte, Sebastian Egger, Stefan Keppeler

Rev. Math. Phys. 29 (2017) 1750027
[ doi:10.1142/S0129055X17500271 | arXiv:1512.05984]

Zusammenfassung

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. 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.