Eur. Phys. J. E (2007) 24: 367-377
https://doi.org/10.1140/epje/i2007-10247-7

Regular Article

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

¹ 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

^* e-mail: michael.schmiedeberg@tu-berlin.de

Received: 13 August 2007
Accepted: 23 November 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.