布朗马达的非均匀高斯跃迁模型

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

提出了布朗马达的非均匀高斯跃迁理论 ,用布朗粒子在多态之间的跃迁模型描述分子马达的定向运动 .假定跃迁速率与位置有关 ,且在跃迁点附近具有高斯函数形式 ,将布朗粒子在x处的概率密度Pm(x ,t)在跃迁点附近展开 ,可以进行任意阶的近似计算 .这一理论涵盖了以往的定点跃迁模型和均匀跃迁模型 .作为具体例子 ,研究了系统在两态之间的跃迁问题 .假定在一个周期内有两个跃迁点 ,讨论了布朗粒子定向运动产生的概率流随温度。

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.