Diffusion and Creep of a Particle in a Random Potential

Details Diffusion and Creep of a Particle in a Random Potential Diffusion and Creep of a Particle in a Random Potential

1998-07-06

arxiv.org/abs/cond-mat/9807090v1

Phys. Rev. B 58 (1998) 213

Physics

Condensed Matter

Superconductivity

6 pages

Scientific paper

10.1103/PhysRevB.58.213

We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of the particle. We determine the $log$-time diffusion ${<{< x^{2}(t)>}_{th}>}_{dis}=A\ln^{\beta} \left ({t}/{t_{r}})$ and relate the prefactor $A,$ the relaxation time $t_{r},$ and the exponent $\beta$ to the details of the (generally non-gaussian) long-range correlated potential. Calculating the moments ${<{< t^{n}>}_{th}>}_{dis}$ of the first-passage time distribution $P(t),$ we reconstruct the large time distribution function itself and draw attention to the phenomenon of intermittency. The results can be easily interpreted in terms of the decay of metastable trapped states. In addition, we present a simple derivation of the mean velocity of a particle moving in a random potential in the presence of a constant external force.

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