The Relaxation-Time Spectrum of Diffusion in a One-Dimensional Random Medium: an Exactly Solvable Case
- 15 March 1987
- journal article
- Published by IOP Publishing in Europhysics Letters
- Vol. 3 (6), 653-660
- https://doi.org/10.1209/0295-5075/3/6/002
Abstract
The asymmetric diffusion of a particle in a random one-dimensional medium can be described by a model of random potential with positive spectrum closely linked to supersymmetric quantum mechanics. We obtain analytical expressions for the density of states ρ(ε) (inverse relaxation time spectrum). This allows us to compute the averaged probability of return at any time. At zero energy ρ(ε) exhibits a variety of singular behaviours with a continuously varying exponent. This corresponds to the different phases of the diffusion problem at large time, including Sinaï's behaviour x2(t) = C ln4t. The validity of the dynamical-scaling assumption is discussed.Keywords
This publication has 17 references indexed in Scilit:
- Relationship between Classical Diffusion, 1/ω Noise and the Motion of a Quantum ParticleEurophysics Letters, 1986
- Relationship between Classical Motion in Random Media and Quantum LocalizationPhysical Review Letters, 1986
- Multidimensional random walks in random environments with subclassical limiting behaviorCommunications in Mathematical Physics, 1986
- Velocity and diffusion constant of a periodic one-dimensional hopping modelJournal of Statistical Physics, 1983
- Random Walk in a Random Environment andNoisePhysical Review Letters, 1983
- On the interpretation of 1/f noiseCommunications in Mathematical Physics, 1983
- Classical Diffusion on a Random ChainPhysical Review Letters, 1982
- Dynamical breaking of supersymmetryNuclear Physics B, 1981
- Excitation dynamics in random one-dimensional systemsReviews of Modern Physics, 1981
- Random Walks in a Random EnvironmentThe Annals of Probability, 1975