A Gutzwiller trace formula for large hermitian matrices
Autor: | Bolte, Jens, Egger, Sebastian, Keppeler, Stefan |
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Rok vydání: | 2015 |
Předmět: | |
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 |
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