Two-level correlation function of critical random-matrix ensembles

E. Cuevas

doi:10.1103/PhysRevB.71.024205

paper

Two-level correlation function of critical random-matrix ensembles

arXiv:cond-mat/0404474 · doi:10.1103/PhysRevB.71.024205

Abstract

The two-level correlation function $R_{d, β} (s)$ of $d$ -dimensional disordered models ( $d = 1$ , 2, and 3) with long-range random-hopping amplitudes is investigated numerically at criticality. We focus on models with orthogonal ( $β = 1$ ) or unitary ( $β = 2$ ) symmetry in the strong ( $b^{d} ≪ 1$ ) coupling regime, where the parameter $b^{- d}$ plays the role of the coupling constant of the model. It is found that $R_{d, β} (s)$ is of the form $R_{d, β} (s) = 1 + δ (s) - F_{β} (s^{β} / b^{d β})$ , where $F_{1} (x) = erfc (a_{d, β} x)$ and $F_{2} (x) = exp (- a_{d, β} x^{2})$ , with $a_{d, β}$ being a numerical coefficient depending on the dimensionality and the universality class. Finally, the level number variance and the spectral compressibility are also considerded.

RevTex4, 7 two-column pages, 6 .eps figures, 1 table. A new section devoted to the spectral compressibility added. To be published in Phys. Rev. B

Two-level correlation function of critical random-matrix ensembles

Abstract

References in corpus (49)

Cited by in corpus (6)