Universal properties of interacting Brownian motors

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 tim e-dependent asymmetric potential and thermal noise. We consider hen the col lective behavior of a finite density of such motors that move on it line an d interact with each other through excluded volume interactions. We show th at thr 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 int eracting Brownian motors an governed by the Kardar-Parisi-Zhang universalit y class [Phys. Rev. Lat. 56, 889 (1986)]. We demonstrate numerically that t he effective noise governing the stochastic dynamics in a coarse-grained ve rsion of our model has short-range spatial correlations. Our results should be applicable to a wide variety of models for Brownian motors with short-r ange interactions. [S1063-651X(99)01802-4].