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Random matrix theory of the energy-level statistics of disordered systems at the Anderson transition

Abstract

We consider a family of random matrix ensembles (RME) invariant under similarity transformations and described by the probability density P(H) exp[-TrV(H)]. Dyson`s mean field theory (MFT) of the corresponding plasma model of eigenvalues is generalized to the case of weak confining potential, V(is an element of) {approx} A/2 ln{sup 2}(is an element of). The eigenvalue statistics derived from MFT are shown to deviate substantially from the classical Wigner-Dyson statistics when A < 1. By performing systematic Monte Carlo simulations on the plasma model, we compute all the relevant statistical properties of the RME with weak confinement. For A{sub c} approx. 0.4 the distribution function of the level spacings (LSDF) coincides in a large energy window with the energy LSDF of the three dimensional Anderson model at the metal-insulator transition. For the same A = A{sub c}, the RME eigenvalue-number variance is linear and its slope is equal to 0.32 {+-} 0.02, which is consistent with the value found for the Anderson model at the critical point. (author). 51 refs, 10 figs.
Authors:
Publication Date:
Sep 01, 1995
Product Type:
Technical Report
Report Number:
IC-95/278
Reference Number:
SCA: 661300; 665000; PA: AIX-27:023379; EDB-96:049011; NTS-96:015387; SN: 96001554766
Resource Relation:
Other Information: PBD: Sep 1995
Subject:
66 PHYSICS; PHASE TRANSFORMATIONS; MEAN-FIELD THEORY; MONTE CARLO METHOD; ANALYTICAL SOLUTION; CORRELATION FUNCTIONS; ELECTRON GAS; ENERGY LEVELS; ENTROPY; ONE-DIMENSIONAL CALCULATIONS; RANDOMNESS; STATISTICAL MODELS; THEORETICAL DATA
OSTI ID:
194029
Research Organizations:
International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ON: DE96617515; TRN: XA9640927023379
Availability:
INIS; OSTI as DE96617515
Submitting Site:
INIS
Size:
42 p.
Announcement Date:

Citation Formats

Canali, C M. Random matrix theory of the energy-level statistics of disordered systems at the Anderson transition. IAEA: N. p., 1995. Web.
Canali, C M. Random matrix theory of the energy-level statistics of disordered systems at the Anderson transition. IAEA.
Canali, C M. 1995. "Random matrix theory of the energy-level statistics of disordered systems at the Anderson transition." IAEA.
@misc{etde_194029,
title = {Random matrix theory of the energy-level statistics of disordered systems at the Anderson transition}
author = {Canali, C M}
abstractNote = {We consider a family of random matrix ensembles (RME) invariant under similarity transformations and described by the probability density P(H) exp[-TrV(H)]. Dyson`s mean field theory (MFT) of the corresponding plasma model of eigenvalues is generalized to the case of weak confining potential, V(is an element of) {approx} A/2 ln{sup 2}(is an element of). The eigenvalue statistics derived from MFT are shown to deviate substantially from the classical Wigner-Dyson statistics when A < 1. By performing systematic Monte Carlo simulations on the plasma model, we compute all the relevant statistical properties of the RME with weak confinement. For A{sub c} approx. 0.4 the distribution function of the level spacings (LSDF) coincides in a large energy window with the energy LSDF of the three dimensional Anderson model at the metal-insulator transition. For the same A = A{sub c}, the RME eigenvalue-number variance is linear and its slope is equal to 0.32 {+-} 0.02, which is consistent with the value found for the Anderson model at the critical point. (author). 51 refs, 10 figs.}
place = {IAEA}
year = {1995}
month = {Sep}
}