Effect of two asymmetries on current of a Brownian particle

A Brownian particle in an asymmetric periodic potential and subjected to an asymmetric dichotomous noise was investigated. In the frame of Fokker-Planck equation, exact expression of current of the system was derived. By means of numerical calculations, the results indicate that: (i) as the symmetry of either potential or noise is broken, a steady current will form; (ii) as the two symmetries are broken simultaneously, the current does not always appear, dependent on values of symmetric parameters of the potential and the noise; (iii) the current exhibits non-monotonic behavior as a function of symmetric parameter of the potential, while monotonic behavior as a function of symmetric parameter of the noise; (iv) in the case the potential symmetry is not broken seriously, the current is greatly influenced on by the noise symmetric parameter; (v) absolute values of the current as a function of height of potential barrier first increase then approach to saturation as the spatial potential is symmetric, while varies monotonically as the dichotomous noise is symmetric. In addition, the planes of the two symmetric parameters, which determine directions of the current, are drawn.