Statistical properties of the time evolution of complex systems. I

Details Statistical properties of the time evolution of complex systems. I Statistical properties of the time evolution of complex systems. I

1997-09-05

arxiv.org/abs/cond-mat/9709070v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

7 pages LaTeX

Scientific paper

The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit the return amplitude to the initial state and the transition amplitude to any other state of Hilbert space are Gaussian distributed. We further compute the exact first and second moments of the distributions. The return and transition probabilities turn out to be non self-averaging quantities with a Poisson distribution. Departures from this universal behaviour are also discussed.

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