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A New Window Onto Quantum Chaos

John Evans·Fredrick Michael
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Abstract

In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parameterized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian orthogonal ensemble (GOE) results are recovered. The relevant level spacing distribution is derived and one obtains a suitably generalized non-extensive Wigner distribution which depends on the value of the tunable non-extensivity parameter q. This non-extensive Wigner distribution can be seen to be a one-parameter level-spacing distribution that allows one to interpolate between chaotic and nearly integrable regimes.

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John Evans, Fredrick Michael. 2002-08-07. A New Window Onto Quantum Chaos. https://arxiv.org/abs/cond-mat/0208151

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