Distribution of velocities and acceleration for a particle in
Brownian correlated disorder: inertial case
Pierre Le Doussal, Aleksandra Petkovic, Kay Jörg Wiese
CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France.
Abstract
We study the motion of an elastic object driven in a disordered environment in presence of both
dissipation and inertia. We consider random forces with the statistics
of random walks and reduce
the problem to a single degree of freedom. It is the extension of the mean field ABBM model
in presence of an inertial mass m. While the ABBM model can be solved exactly, its extension
to inertia exhibits complicated history dependence due to oscillations and backward motion. The
characteristic scales for avalanche motion are studied from numerics and qualitative arguments. To
make analytical progress we consider two variants which coincide with the original model whenever
the particle moves only forward. Using a combination of analytical and numerical methods together
with simulations, we characterize the distributions of instantaneous acceleration and velocity, and
compare them in these three models. We show that for large driving velocity, all three models share
the same large-deviation function for positive velocities, which is obtained analytically for small and
large m, as well as for m = 6/25. The effect of small additional thermal and quantum fluctuations
can be treated within an approximate method.
arXiv:1203.5620 [pdf]
Phys. Rev. E 85 (2012) 061116 [pdf]
Copyright (C) by Kay Wiese. Last edited March 27, 2012.