2000/11/02 by Bruno Eckhardt, Eckhardt, Bruno, Uzy Smilansky +1
Computer Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum chaos and dynamical systems #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0011004
12 pages
arxiv created 2000/11/02 · openalex publication_date 2000/11/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum within a prescribed and finite energy interval. The resulting semiclassical expression involves a finite number of periodic orbits whose energies are in the considered interval. Higher order corrections which reflect the sharp restriction of the spectrum to an interval are explicitely given. The relation to Fourier methods for extracting semiclassical spectra, such as harmonic inversion, is worked out. The constraints due to the finite dimension of the Hilbert space and the unitarity of the restricted quantum evolution operator are important ingredients in this context.