Nonlinear Response of Brownian Motion's Particles in Periodic Potential

The Brownian motion of particles in a periodic potential driven by an external force is an important model for explaining the mobility of superionic conductors.By using matrix continued fraction method,we solve the corresponding Fokker-Planck equation of electron and obtain the Current-Voltage characteristic of a Josephson tunneling junction and the nonlinear relation on electricity transportation of the phonon-electron,which coincide with the experiments relation very well.