分数阶广义Langevin方程方法求解单列扩散问题
Fractional generalized Langevin equation approach to single-file diffusion
摘要：
采用分数阶广义Langevin方程描述单流扩散过程，该方程具有外力作用。结果表明，当外力按幂律变化时，当适当选择分数阶广义Langevin方程的参数时，分数阶广义Langevin方程的解给出了单列扩散均方位移的正确的短时和长时行为.通过考虑分数阶广义朗之万方程的一些特殊情况，得到了一类新的单列扩散均方位移的封闭解析表达式。简单地考虑了与单列扩散相关的有效Fokker-Planck方程。
英文摘要：
Fractional generalized Langevin equation with external force is used to model single-file diffusion. It is found that for external force that varies with power law the solution for such a fractional Langevin equation gives the correct short and long time behavior for the mean square displacement of single-file diffusion when appropriate choice of parameters associated with fractional generalized Langevin equation are used. By considering some special cases of the fractional generalized Langevin equation, a new class of closed analytic expressions for the mean square displacement of single-file diffusion can be obtained. The effective Fokker-Planck equation associated with single-file diffusion is briefly considered.
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