Eur. Phys. J. E 24, 367-377 (2007)
DOI: 10.1140/epje/i2007-10247-7

Brownian particles in random and quasicrystalline potentials: How they approach the equilibrium

M. Schmiedeberg¹, J. Roth² and H. Stark<sup>1

1</sup>  Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623, Berlin, Germany
²  Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70550, Stuttgart, Germany

michael.schmiedeberg@tu-berlin.de

(Received 13 August 2007 / Published online 18 January 2008)

Abstract

We study the Brownian motion of an ensemble of single colloidal particles in a random square and a quasicrystalline potential when they start from non-equlibrium. For both potentials, Brownian dynamics simulations reveal a widespread subdiffusive regime before the diffusive long-time limit is reached in thermal equilibrium. We develop a random trap model based on a distribution for the depths of trapping sites that reproduces the results of the simulations in detail. Especially, it gives analytic formulas for the long-time diffusion constant and the relaxation time into the diffusive regime. Aside from detailed differences, our work demonstrates that quasicrystalline potentials can be used to mimic aspects of random potentials.

PACS
82.70.Dd - Colloids.
05.40.Jc - Brownian motion.
61.44.Br - Quasicrystals.

Correspondence: michael.schmiedeberg@tu-berlin.de


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2008

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