2015/12/31 by Jens Bolte, Sebastian Egger, Stefan Keppeler · 2 citations
Mathematics · Physics and Astronomy · #Eigenvalues and eigenvectors #Hermitian matrix #Hilbert space #Mathematical physics #Mathematics #Phase space #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Semiclassical physics #Spectral Theory in Mathematical Physics #TRACE (psycholinguistics) #Unitary matrix #Unitary state #math-ph #math.MP #nlin.CD
paper · pdf · doi:10.1142/s0129055x17500271
published in Reviews in Mathematical Physics 29(08), 1750027 (World Scientific) · 41 pages; extended introduction; added appendix an comparison of anti-Wick and Weyl quantisation
openalex publication_date 2017/07/31 · arxiv created 2017/08/03 · arxiv updated 2017/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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.