Level Spacing Distribution of Critical Random Matrix Ensembles

Details Level Spacing Distribution of Critical Random Matrix Ensembles Level Spacing Distribution of Critical Random Matrix Ensembles

1998-07-21

arxiv.org/abs/cond-mat/9807282v4

Phys.Rev. E58 (1998) R6915-R6918

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 1 figure, REVTeX; restriction on the parameter stressed, figure replaced, refs added (v2); typos (factors of pi) in (

Scientific paper

10.1103/PhysRevE.58.R6915

We consider unitary invariant random matrix ensembles which obey spectral statistics different from the Wigner-Dyson, including unitary ensembles with slowly (~(log x)^2) growing potentials and the finite-temperature fermi gas model. If the deformation parameters in these matrix ensembles are small, the asymptotically translational-invariant region in the spectral bulk is universally governed by a one-parameter generalization of the sine kernel. We provide an analytic expression for the distribution of the eigenvalue spacings of this universal asymptotic kernel, 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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