Current reversal and exclusion processes with history-dependent random walks
Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics Ludwig-Maximilians-Universität München - Theresienstraße 37, D-80333 München, Germany, EU
2 Department of Chemistry, Rice University - Houston, TX 77005, USA
Accepted: 17 June 2011
A class of exclusion processes in which particles perform history-dependent random walks is introduced, stimulated by dynamic phenomena in some biological and artificial systems. The particles locally interact with the underlying substrate by breaking and reforming lattice bonds. We determine the steady-state current on a ring, and find current-reversal as a function of particle density. This phenomenon is attributed to the non-local interaction between the walkers through their trails, which originates from strong correlations between the dynamics of the particles and the lattice. We rationalize our findings within an effective description in terms of quasi-particles which we call front barriers. Our analytical results are complemented by stochastic simulations.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.-r – Probability theory, stochastic processes, and statistics / 87.10.Mn – Stochastic modeling
© EPLA, 2011