Chew L Y, Ting Christopher
Department of Physics, National University of Singapore, Singapore 117542.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 1):031103. doi: 10.1103/PhysRevE.69.031103. Epub 2004 Mar 16.
We show that the Perron-Frobenius equation of microscopic chaos based on double symmetric maps leads to an inhomogeneous Smoluchowski equation with a source term. Our perturbative analysis reveals that the source term gives rise to a directed current for a strongly damped particle in a spatially periodic potential. In addition, our result proves that in the zeroth-order limit, the position distribution of the particle obeys the Smoluchowski equation even though the fluctuating force is deterministic.
我们表明，基于双对称映射的微观混沌的Perron-Frobenius方程会导致一个带有源项的非齐次Smoluchowski方程。我们的微扰分析表明，对于处于空间周期势中的强阻尼粒子，源项会产生一个定向电流。此外，我们的结果证明，在零阶极限下，即使涨落力是确定性的，粒子的位置分布仍服从Smoluchowski方程。
