Non-Universality in Random Matrix Ensembles with Soft Level Confinement

Abstract

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.

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

References in corpus (1)

• Universal Spectral Correlations at the Mobility Edge

Cited by in corpus (11)

• Random Matrix Theories in Quantum Physics: Common Concepts
• New Class of Random Matrix Ensembles with Multifractal Eigenvectors
• Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles
• Spectral Correlations from the Metal to the Mobility Edge
• Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition
• Unitary Random-Matrix Ensemble with Governable Level Confinement
• New Critical Matrix Models and Generalized Universality
• Weak and strong confinement in the Freud random matrix ensemble and gap probabilities
• Universality of a family of Random Matrix Ensembles with logarithmic soft-confinement potentials
• Spectral properties of a generalized chGUE
• Emergent random matrix universality in quantum operator dynamics