Goussev, Arseni and Waltner, Daniel and Richter, Klaus and Jalabert, Rodolfo A. (2008) Loschmidt echo for local perturbations: non-monotonic cross-over from the Fermi-golden-rule to the escape-rate regime. NEW JOURNAL OF PHYSICS, 10: 093010. ISSN 1367-2630,
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We address the sensitivity of quantum mechanical time evolution by considering the time decay of the Loschmidt echo (LE) (or fidelity) for local perturbations of the Hamiltonian. Within a semiclassical approach, we derive analytical expressions for the LE decay for chaotic systems for the whole range from weak to strong local perturbations and identify different decay regimes which complement those known for the case of global perturbations. For weak perturbations, a Fermi-golden-rule (FGR)-type behavior is recovered. For strong perturbations, the escape-rate regime is reached, where the LE decays exponentially with a rate independent of the perturbation strength. The transition between the FGR regime and the escape-rate regime is non-monotonic, i.e. the rate of the exponential time-decay of the LE oscillates as a function of the perturbation strength. We further perform extensive quantum mechanical calculations of the LE based on numerical wave packet evolution, which strongly support our semiclassical theory. Finally, we discuss in some detail possible experimental realizations for observing the predicted behavior of the LE.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CHAOTIC SYSTEMS; HYPERBOLIC SYSTEMS; QUANTUM MOTION; ATOM-OPTICS; BILLIARDS; FIDELITY; DECAY; APPROXIMATION; DECOHERENCE; ATTRACTORS; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 26 Oct 2020 07:10 |
| Last Modified: | 26 Oct 2020 07:10 |
| URI: | https://pred.uni-regensburg.de/id/eprint/30292 |
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