Universal properties of interacting Brownian motors

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Abstract
We study the effects of interactions in ratchet models for one-dimensional Brownian motors. In these models, directed motion of a single particle (the motor) is produced by subjecting it to the action of a one-dimensional time-dependent asymmetric potential and thermal noise. We consider here the collective behavior of a finite density of such motors that move on a line and interact with each other through excluded volume interactions. We show that the density-density correlation function, calculated in the steady state, exhibits dynamical scaling at long wavelengths and times. Our Monte Carlo simulations support the conjecture that the hydrodynamic properties of interacting Brownian motors are governed by the Kardar-Parisi-Zhang universality class [Phys. Rev. Lett. 56, 889 (1986)]. We demonstrate numerically that the effective noise governing the stochastic dynamics in a coarse-grained version of our model has short-range spatial correlations. Our results should be applicable to a wide variety of models for Brownian motors with short-range interactions.

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