Turek, Marko and Spehner, Dominique and Müller, Sebastian and Richter, Klaus (2005) Semiclassical form factor for spectral and matrix element fluctuations of multi-dimensional chaotic systems. Physical Review E 71, 016210-1-016210-15.
Download (429kB) - Repository staff only
Other URL: http://link.aps.org/abstract/PRE/v71/e016210
We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators 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 the generalized form factor. We show that the dependence on the rescaled time in units of the Heisenberg time is universal for both the spectral and the generalized form factor. Furthermore, we derive a relation between the generalized form factor and the classical time- correlation function of the Weyl symbols of the quantum operators.
|Institutions:||Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter|
|Projects:||Graduiertenkolleg Nichtlinearität und Nichtgleichgewicht|
|Subjects:||500 Science > 530 Physics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Deposited On:||20 Mar 2007|
|Last Modified:||20 Jul 2011 20:58|