Level Spacing Distribution of Crossover Random Matrix Ensembles

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  • 21 July 1998
Abstract
We consider unitary invariant random matrix ensembles which interpolates chaotic (Wigner-Dyson) and regular (Poisson) statistics. The spectral bulk of such models, including unitary ensembles with slowly (~(log x)^2) growing potentials and the finite-temperature fermi gas model, is universally governed by a one-parameter generalization of the sine kernel, which also describes the 3D Anderson hamiltonian at the metal/insulator transition point. We provide an analytic expression for the distribution of the eigenvalue spacing of these ensembles, which is a hybrid of the Wigner-Dyson and the Poisson distributions, by determining the Fredholm determinant of the universal kernel in terms of a Painleve VI transcendental function.

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