02.07.2008 (Wednesday)

Random-Matrix Theory within Superstatistics

Regular Seminar Adel Abul-Magd (Sinai University)

11:00 Brunel U.
room M128

In analogy to Beck and Cohen's superstatistics (1), we connect the canonical Gaussian ensembles of the random-matrix theory (RMT) to their superstatistical generalizations through the fluctuation of an intensive parameter, the local density of states (2). On one hand, the superstatistical RMT, seen from the present perspective, may bear interest per se because of the additional nontrivial fluctuations introduced in a simple model. On the other hand, it may constitute a useful statistical paradigm for the analysis of the spectral fluctuations of systems with mixed regular-chaotic dynamics. In contrast to other proposals for applying RMT to mixed dynamics, the superstatistical approach yields ensemble of matrices, which are invariant with respect to base transformation. The formalism has been checked by the analysis of experimental resonance spectra of mixed microwave billiards (3). The spectra for each billiard are represented as time series in which the level order plays the role of time. Each series is shown to have two relaxation times as required by superstatistics, which involves the folding of two distribution functions. Analysis of the time series suggests that the superstatistical parameter has an inverse-chi-square distribution. The experimental distribution nearest-neighbor level spacings and strength functions agree with the corresponding predicted distributions. (1) C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003). (2) A.Y. Abul-Magd, Phys.Rev. E 71, 066207 (2005). (3) A.Y. Abul-Magd, B. Dietz, T. Friedrich, and A. Richter, Phys. R