A nonuniform ratchet model with Gauss-transition rates for Brownian motor

A nonuniform ratchet model with Gauss-transition rates is proposed to discuss the directional motion of Brownian particles in an asymmetrical periodic potential. It is assumed that the particles experience several internal states in a single mechanical-chemical circle. In this model, the transition rates between different states are position-dependent, which have the form of Gaussian function. For any internal states, the probability distribution as a function of time and position may be expanded near the transition points to any rank if necessary. Finally, the focus of our study is concentrated on a two-state model, in which we choose ( M, K) = (2, 2) and calculate the average current as a function of the transition width, temperature and transition rate. It is revealed that the transition width influences the current greatly.