## 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.

## 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}

}

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}

}