Waltner, Daniel and Richter, Klaus (2019) Towards a semiclassical understanding of chaotic single- and many-particle quantum dynamics at post-Heisenberg time scales. PHYSICAL REVIEW E, 100 (4): 042212. ISSN 2470-0045, 2470-0053
Full text not available from this repository.Abstract
Despite considerable progress during the past decades in devising a semiclassical theory for classically chaotic quantum systems a quantitative semiclassical understanding of their dynamics at late times (beyond the so-called Heisenberg time T-H) is still missing. This challenge, corresponding to resolving spectral structures on energy scales below the mean level spacing, is intimately related to the quest for semiclassically restoring unitary quantum evolution. Guided through insights for quantum graphs we devise a periodic-orbit resummation procedure for spectra of quantum chaotic systems invoking periodic-orbit self-encounters as the structuring element of a hierarchical phase space dynamics. Quantum unitarity is reflected in real-valued spectral determinants with zeros giving discrete energy levels. We propose a way to purely semiclassically construct such real spectral determinants based on two major underlying mechanisms. (i) Complementary contributions to the spectral determinant from regrouped pseudo-orbits of duration T < T-H and T-H - T are complex conjugate to each other. (ii) Contributions from long periodic orbits involving multiple traversals along shorter orbits cancel out. We furthermore discuss implications for interacting N-particle quantum systems with a chaotic classical large-N limit that have recently attracted particular interest in the context of many-body quantum chaos.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SPECTRAL STATISTICS; PERIODIC-ORBITS; QUANTIZATION; GRAPHS; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 Mar 2020 09:25 |
| Last Modified: | 25 Mar 2020 09:25 |
| URI: | https://pred.uni-regensburg.de/id/eprint/25993 |
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