Turek, Marko and Spehner, Dominique and Muller, Sebastian and Richter, Klaus (2005) Semiclassical form factor for spectral, and matrix element fluctuations of multidimensional chaotic systems. PHYSICAL REVIEW E, 71 (1): 016210. ISSN 1063-651X,
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We present a semiclassical calculation of the generalized form factor K-ab(tau) which characterizes the fluctuations of matrix elements of the operators (a) over cap and (b) over cap in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some recently developed techniques for the spectral form factor of systems with hyperbolic and ergodic underlying classical dynamics and f=2 degrees of freedom, that allow us to go beyond the diagonal approximation. First we extend these techniques to systems with f>2. Then we use these results to calculate K-ab(tau). We show that the dependence on the rescaled time tau (time in units of the Heisenberg time) is universal for both the spectral and the generalized form factor. Furthermore, we derive a relation between K-ab(tau) and the classical time-correlation function of the Weyl symbols of (a) over cap and (b) over cap.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PERIODIC-ORBITS; DIAGONAL APPROXIMATION; HYPERBOLIC SYSTEMS; QUANTUM-SYSTEMS; TIME-REVERSAL; TRACE FORMULA; EIGENFUNCTIONS; ERGODICITY; STATISTICS; STATES; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 21 Jun 2021 06:58 |
| Last Modified: | 21 Jun 2021 06:58 |
| URI: | https://pred.uni-regensburg.de/id/eprint/36812 |
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