Influence Of The Entropic Barrier And The Space Dependent Friction Coefficient On The Transport Of Brownian Particles

Fluctuation-Dissipation Theorem(FDT) is an important theory in the non-equilibrium statistical physics. It can well explain the problems of the energy conversion and particles transport process where fluctuations play a major role:fluids, mesoscopic and biological systems. Brownian motion is a significant model of FDT, the main research is the energy conversion of thermal fluctuations and transport process of micro-particles far from equilibrium. The investigation on the transport processes of Brownian particle provides theoretical guidance for developing molecular motors. In the present thesis we will investigate the transport process of Brownian particles in two typical environments:one is in the existence of entropy barrier; the other is in the space dependent friction coefficient.In chapterâ… we abstractly introduce the background of Brownian motion, the two well-known models of non-equilibrium physics and the significance of related researches.In chapterâ…¡several methods in the description of the dynamical evolution of Brownian particles are summarized briefly.In chapterâ…¢, a model of a Buttiker-Landauer motor, which is a position dependent temperature-driven Brownian motor, with entropic and energy barriers have been built and behavior of the current of Brownian particles has been studied. It is found that the motion of the Brownian particles is influenced by the shape of the channel. The existence of an entropic barrier can cause an asymmetric current as the flatness ratio of the shape varies. There exists an optimized flatness ratio(nonzero) at which the current reaches its maximum value.In chapterâ…£the relationship between the dynamics of an excess charge carrier evolving in the charge space have been established. The excess charge carrier in the nonlinear resistance is proposed to be a kind of Brownian particles moving in the environment with space distribution friction coefficient. Solving the Fokker-Planck equation of the excess charge carrier the relationship between the Peltier coefficient and the volt-ampere characteristics of the nonlinear resistance has been derived. A semiconductor thermal fluctuation rectifier has been constructed, efficiency of the device and thermal current have been calculated. It is found that the device can't work in reversible conditions.