Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition

Details Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition

1995-09-04

arxiv.org/abs/cond-mat/9509014v1

Physics

Condensed Matter

32 pages, REVTEX 3.0, 10 postscript (uuencoded) figures included

Scientific paper

10.1103/PhysRevB.53.3713

We consider a family of random matrix ensembles (RME) invariant under similarity transformations and described by the probability density $P({\bf H})= \exp[-{\rm Tr}V({\bf H})]$. Dyson's mean field theory (MFT) of the corresponding plasma model of eigenvalues is generalized to the case of weak confining potential, $V(\epsilon)\sim {A\over 2}\ln ^2(\epsilon)$. 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 $A_c\approx 0.4$ the distribution function of the energy-level spacings (LSDF) of this RME coincides in a large energy window with the LSDF of the three dimensional Anderson model at the metal-insulator transition. For the same $A_c$, the variance of the number of levels, $\langle n^2\rangle -\langle n\rangle^2$, in an interval containing $\langle n\rangle$ levels on average, grows linearly with $\langle n\rangle$, and its slope is equal to $0.32 \pm 0.02$, which is consistent with the value found for the Anderson model at the critical point.

Affiliated with

Also associated with

No associations

Rating

Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-356644