Integrable random matrix ensembles

Details Integrable random matrix ensembles Integrable random matrix ensembles

2011-04-19

arxiv.org/abs/1104.3777v1

Nonlinear Sciences

Chaotic Dynamics

32 pages, 8 figures

Scientific paper

We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with a random distribution of momenta and coordinates of the particles. The Lax matrices of these systems yield random matrix ensembles whose joint distribution of eigenvalues can be calculated analytically thanks to integrability of the underlying system. Formulas for spacing distributions and level compressibility are obtained for various instances of such ensembles.

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