Gutierrez, Marta and Brack, Matthias and Richter, Klaus and Sugita, Ayumu (2007) The effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 40 (7). pp. 1525-1543. ISSN 1751-8113,
Full text not available from this repository.Abstract
We present a quantitative semiclassical treatment of the effects of bifurcations on the spectral rigidity and the spectral form factor of a Hamiltonian quantum system defined by two coupled quartic oscillators, which on the classical level exhibits mixed phase space dynamics. We show that the signature of a pitchfork bifurcation is two-fold: beside the known effect of an enhanced periodic orbit contribution due to its peculiar h-dependence at the bifurcation, we demonstrate that the orbit pair born at the bifurcation gives rise to distinct deviations from universality slightly above the bifurcation. This requires a semiclassical treatment beyond the so-called diagonal approximation. Our semiclassical predictions for both the coarse-grained density of states and the spectral rigidity, are in excellent agreement with corresponding quantum-mechanical results.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SEMICLASSICAL TRACE FORMULAS; PERIODIC-ORBITS; UNIFORM APPROXIMATION; DISCRETE SYMMETRIES; INTEGRABLE SYSTEMS; HYPERBOLIC SYSTEMS; QUANTUM-MECHANICS; BOUND SPECTRUM; FLUCTUATIONS; EXPONENTS; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter Physics > Institute of Theroretical Physics > Alumni or Retired Professors > Group Matthias Brack |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Dec 2020 10:10 |
| Last Modified: | 22 Dec 2020 10:10 |
| URI: | https://pred.uni-regensburg.de/id/eprint/33180 |
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