Non-Universality in Random Matrix Ensembles with Soft Level Confinement

Details Non-Universality in Random Matrix Ensembles with Soft Level Confinement Non-Universality in Random Matrix Ensembles with Soft Level Confinement

1994-10-02

arxiv.org/abs/cond-mat/9409123v1

Physics

Condensed Matter

4 pages, REVTEX, 3 postscript figures appended, ICTP/9/94/ckw.1

Scientific paper

10.1103/PhysRevB.51.2831

Two families of strongly non-Gaussian random matrix ensembles (RME) are considered. They are statistically equivalent to a one-dimensional plasma of particles interacting logarithmically and confined by the potential that has the long-range behavior $V(\epsilon)\sim |\epsilon|^{\alpha}$ ($0<\alpha<1$), or $V(\epsilon)\sim \ln^{2}|\epsilon|$. The direct Monte Carlo simulations on the effective plasma model shows that the spacing distribution function (SDF) in such RME can deviate from that of the classical Gaussian ensembles. For power-law potentials, this deviation is seen only near the origin $\epsilon\sim 0$, while for the double-logarithmic potential the SDF shows the cross-over from the Wigner-Dyson to Poisson behavior in the bulk of the spectrum.

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