A Gutzwiller trace formula for large hermitian matrices

Autor:	Bolte, Jens, Egger, Sebastian, Keppeler, Stefan
Rok vydání:	2015
Předmět:	Mathematical Physics Nonlinear Sciences - Chaotic Dynamics
Zdroj:	Rev. Math. Phys. 29 (2017) 1750027
Druh dokumentu:	Working Paper
DOI:	10.1142/S0129055X17500271
Popis:	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. Comment: 41 pages; extended introduction; added appendix an comparison of anti-Wick and Weyl quantisation
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1512.05984 Zobrazit plný text záznamu View this record from Arxiv