7 research outputs found
Dynamics of particles and manifolds in a quenched random force field
We study the dynamics of a directed manifold of internal dimension D in a
d-dimensional random force field. We obtain an exact solution for and a Hartree approximation for finite d. They yield a Flory-like
roughness exponent and a non trivial anomalous diffusion exponent
continuously dependent on the ratio of divergence-free ()
to potential () disorder strength. For the particle (D=0) our results
agree with previous order RG calculations. The time-translational
invariant dynamics for smoothly crosses over to the previously
studied ultrametric aging solution in the potential case.Comment: 5 pages, Latex fil
Anderson localization transition with long-ranged hoppings : analysis of the strong multifractality regime in terms of weighted Levy sums
For Anderson tight-binding models in dimension with random on-site
energies and critical long-ranged hoppings decaying
typically as , we show that the strong multifractality
regime corresponding to small can be studied via the standard perturbation
theory for eigenvectors in quantum mechanics. The Inverse Participation Ratios
, which are the order parameters of Anderson transitions, can be
written in terms of weighted L\'evy sums of broadly distributed variables (as a
consequence of the presence of on-site random energies in the denominators of
the perturbation theory). We compute at leading order the typical and
disorder-averaged multifractal spectra and as a
function of . For , we obtain the non-vanishing limiting spectrum
as . For , this method
yields the same disorder-averaged spectrum of order as
obtained previously via the Levitov renormalization method by Mirlin and Evers
[Phys. Rev. B 62, 7920 (2000)]. In addition, it allows to compute explicitly
the typical spectrum, also of order , but with a different -dependence
for all . As a consequence, we find
that the corresponding singularity spectra and
differ even in the positive region , and vanish at
different values , in contrast to the standard
picture. We also obtain that the saddle value of the Legendre
transform reaches the termination point where
only in the limit .Comment: 13 pages, 2 figures, v2=final versio
Comment on ``Critical Behavior in Disordered Quantum Systems Modified by Broken Time--Reversal Symmetry''
In a recent Letter [Phys. Rev. Lett. 80, 1003 (1998)] Hussein and Pato
employed the maximum entropy principle (MEP) in order to derive interpolating
ensembles between any pair of universality classes in random matrix theory.
They apply their formalism also to the transition from random matrix to Poisson
statistics of spectra that is observed for the case of the Anderson-type
metal-insulator transition. We point out the problems with the latter
procedure.Comment: 1 page in PS, to appear in PRL Sept. 2
Wavefunction and level statistics of random two dimensional gauge fields
Level and wavefunction statistics have been studied for two dimensional
clusters of the square lattice in the presence of random magnetic fluxes.
Fluxes traversing lattice plaquettes are distributed uniformly between - (1/2)
Phi_0 and (1/2) Phi_0 with Phi_0 the flux quantum. All considered statistics
start close to the corresponding Wigner-Dyson distribution for small system
sizes and monotonically move towards Poisson statistics as the cluster size
increases. Scaling is quite rapid for states close to the band edges but really
difficult to observe for states well within the band. Localization properties
are discussed considering two different scenarios. Experimental measurement of
one of the considered statistics --wavefunction statistics seems the most
promising one-- could discern between both possibilities. A real version of the
previous model, i.e., a system that is invariant under time reversal, has been
studied concurrently to get coincidences and differences with the Hermitian
model.Comment: 12 twocolumnn pages in revtex style, 17 postscript figures, to be
published in PRB, send comments to [email protected]