165 research outputs found
Levy flights in quenched random force fields
Levy flights, characterized by the microscopic step index f, are for f<2 (the
case of rare events) considered in short range and long range quenched random
force fields with arbitrary vector character to first loop order in an
expansion about the critical dimension 2f-2 in the short range case and the
critical fall-off exponent 2f-2 in the long range case. By means of a dynamic
renormalization group analysis based on the momentum shell integration method,
we determine flows, fixed point, and the associated scaling properties for the
probability distribution and the frequency and wave number dependent diffusion
coefficient. Unlike the case of ordinary Brownian motion in a quenched force
field characterized by a single critical dimension or fall-off exponent d=2,
two critical dimensions appear in the Levy case. A critical dimension (or
fall-off exponent) d=f below which the diffusion coefficient exhibits anomalous
scaling behavior, i.e, algebraic spatial behavior and long time tails, and a
critical dimension (or fall-off exponent) d=2f-2 below which the force
correlations characterized by a non trivial fixed point become relevant. As a
general result we find in all cases that the dynamic exponent z, characterizing
the mean square displacement, locks onto the Levy index f, independent of
dimension and independent of the presence of weak quenched disorder.Comment: 27 pages, Revtex file, 17 figures in ps format attached, submitted to
Phys. Rev.
Driven diffusive system with non-local perturbations
We investigate the impact of non-local perturbations on driven diffusive
systems. Two different problems are considered here. In one case, we introduce
a non-local particle conservation along the direction of the drive and in
another case, we incorporate a long-range temporal correlation in the noise
present in the equation of motion. The effect of these perturbations on the
anisotropy exponent or on the scaling of the two-point correlation function is
studied using renormalization group analysis.Comment: 11 pages, 2 figure
Glassy trapping of manifolds in nonpotential random flows
We study the dynamics of polymers and elastic manifolds in non potential
static random flows. We find that barriers are generated from combined effects
of elasticity, disorder and thermal fluctuations. This leads to glassy trapping
even in pure barrier-free divergenceless flows
(). The physics is described by a new RG fixed point at finite
temperature. We compute the anomalous roughness and dynamical
exponents for directed and isotropic manifolds.Comment: 5 pages, 3 figures, RevTe
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