A Gutzwiller trace formula for large hermitian matrices

作者：Bolte Jens^*; Egger Sebastian; Keppeler Stefan

来源：Reviews in Mathematical Physics, 2017, 29(8): 1750027.

DOI：10.1142/S0129055X17500271

• Gutzwiller trace formula
• Weyl quantization
• semiclassical approximations
• toroidal phase space
• difference operators

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 Schrodinger equation. In the framework of Weyl quantization, 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 quantization condition for eigenvalues as well as some simple examples.

• 出版日期2017-9