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Random walk on a random walk

Ryszard Kutner 1,  Klaus W. Kehr 2

1. Faculty of Physics, University of Warsaw (FPUW), Pasteura 5, Warsaw 02-093, Poland
2. Institut fur Festkoerperforschungs, Forschungszentrum Jülich (FZJ), Wilhelm-Johnen-Straße, Jülich 52428, Germany

Abstract
The authors investigate the random walk of a particle on a one-dimensional chain which has been constructed by a random-walk procedure. Exact expressions are given for the mean-square displacement and the fourth moment after n steps. The probability density after n steps is derived in the saddle-point approximation, for large n. These quantities have also been studied by numerical simulation. The extension to continuous time has been made where the particle jumps according to a Poisson process. The exact solution for the self-correlation function has been obtained in the Fourier and Laplace domain. The resulting frequency-dependent diffusion coefficient and incoherent dynamical structure factor have been discussed. The model of random walk on a random walk is applied to self-diffusion in the concentrated one-dimensional lattice gas where the correct asymptotic behavior is found.

Physica A 110, 535 (1982).

 

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Presentation: Article at Econophysics group of Ryszard Kutner, by Ryszard Kutner
See On-line Journal of Econophysics group of Ryszard Kutner

Submitted: 2016-03-09 19:49
Revised:   2016-03-09 19:55