Towards a Non-extensive Random Matrix Theory

Details Towards a Non-extensive Random Matrix Theory Towards a Non-extensive Random Matrix Theory

2002-07-19

arxiv.org/abs/cond-mat/0207472v3

Physics

Condensed Matter

Statistical Mechanics

9 pages, 3 figures

Scientific paper

In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parametrized 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 nonextensive 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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