2,377 research outputs found
Eigenfunction entropy and spectral compressibility for critical random matrix ensembles
Based on numerical and perturbation series arguments we conjecture that for
certain critical random matrix models the information dimension of
eigenfunctions D_1 and the spectral compressibility chi are related by the
simple equation chi+D_1/d=1, where d is the system dimensionality.Comment: 4 pages, 3 figure
Spectral correlations in the crossover between GUE and Poisson regularity: on the identification of scales
Motivated by questions of present interest in nuclear and condensed matter
physics we consider the superposition of a diagonal matrix with independent
random entries and a GUE. The relative strength of the two contributions is
determined by a parameter suitably defined on the unfolded scale.
Using results for the spectral two-point correlator of this model obtained in
the framework of the supersymmetry method we focus attention on two different
regimes. For << 1 the correlations are given by Dawson's integral
while for >> 1 we derive a novel analytical formula for the two-point
function. In both cases the energy scales, in units of the mean level spacing,
at which deviations from pure GUE behavior become noticable can be identified.
We also derive an exact expansion of the local level density for finite level
number.Comment: 15 pages, Revtex, no figures, to be published in special issue of J.
Math. Phys. (1997
Infrared catastrophe in two-quasiparticle collision integral
Relaxation of a non-equilibrium state in a disordered metal with a
spin-dependent electron energy distribution is considered. The collision
integral due to the electron-electron interaction is computed within the
approximation of a two-quasiparticle scattering. We show that the spin-flip
scattering processes with a small energy transfer may lead to the divergence of
the collision integral for a quasi one-dimensional wire. This divergence is
present only for a spin-dependent electron energy distribution which
corresponds to the total electron spin magnetization M=0 and only for non-zero
interaction in the triplet channel. In this case a non-perturbative treatment
of the electron-electron interaction is needed to provide an effective infrared
cut-off.Comment: 6 pages, 3 figure
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