Article details

Title:: Mode fluctuations as fingerprints of chaotic and non-chaotic systems
Authors:: R. Aurich, A. Bäcker and F. Steiner
Journal:: Int. J. Mod. Phys. B 11 (1997) 805-849
Abstract:: The mode-fluctuation distribution P(W) is studied for chaotic as well as for non-chaotic quantum billiards. This statistic is discussed in the broader framework of the E(k, L) functions being the probability of finding k energy levels in a randomly chosen interval of length L, and the distribution of n(L), where n(L) is the number of levels in such an interval, and their cumulants c_k(L). It is demonstrated that the cumulants provide a possible measure for the distinction between chaotic and non-chaotic systems. The vanishing of the normalized cumulants C_k, k > 2, implies a Gaussian behaviour of P(W), which is realized in the case of chaotic systems, whereas non-chaotic systems display non-vanishing values for these cumulants leading to a non-Gaussian behaviour of P(W). For some integrable systems there exist rigorous proofs of the non-Gaussian behaviour which are also discussed. Our numerical results and the rigorous results for integrable systems suggest that a clear fingerprint of chaotic systems is provided by a Gaussian distribution of the mode-fluctuation distribution P(W).
Download:: Please refer to the above published version.
(The preprint version of this article can be obtained as
Ulm report ULM-TP/96-2 (1996), or as chao-dyn 9608016.)