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Keywords:

  • Noise induced transport;
  • Fokker-Planck equation;
  • molecular motors

Abstract

We study the overdamped motion of a particle in a one-dimensional periodic potential driven by a stochastic force. If the stochastic force is correlated in time (non-white), and if the potential has no inversion symmetry, a current is generated. In the case of a piecewise linear potential we obtain a closed expression for the current as a ratio of two determinants. This allows us to calculate the current as a function of the noise strength, the correlation time and the temperature of the system for several stochastic processes. We examine several limiting situations. Depending on the statistics of the noise process, the direction of the current may change. Two different mechanisms for this effect are discussed.