Diffusion Of Brownian Particles Driven By Ornstein-Uhlenbeck Noise In One Dimensional Periodic Potential

In this thesis,the diffusion behavior of Brownian particles in a tilted periodic potential driven by an internal white noise and an external OU noise and the diffusion behavior of Brownian particles in periodic and tilted periodic potentials driven by an internal OU noise are studied.The physical mechanisms of the results are explored.In the first part,we study the diffusion of Brownian particles driven by an external OU noise in a tilted periodic potential by numerical simulation.The numerical simulation results show that the diffusion coefficient is a non-monotonic function of the external noise correlation time at large bias force.This can be attributed to that the larger bias force accelerates the transport of particles from the bottom of the potential well to the barrier,the number of particles at the top of the barrier grows,and the second moment of coordinate and velocity in potential barrier region in harmonic approximation are non-monotonic function of the noise correlation time.When the bias force is absent or small,this nonmonotonicity degenerates into a monotonic decreasing function.This is because it is more difficulty for the particles to climb up on the top of the barrier,and the rise of the second moment with the noise correlation time can't compensate for the decrease of the escape rate of the trapped particles in the potential well.The diffusion coefficient of the Brownian particles is a negative power of the damping coefficient,and the external OU noise and bias force increase the absolute value of the power.New physical mechanisms were proposed to explain that the bia s force increases the diffusion coefficient in mid-to-large damping.This is because the particles in the source potential well are moved by the bias force to a position where the potential energy is higher and the local harmonic frequency is lower,so that the state density is higher and the entropy increases.This can be equivalent to an unbiased system which has an effective temperature above environment temperature.When the bias force is close to but less than its critical value,some novel behaviors of diffusion are found.When the internal noise intensity is small and the external noise is absent,the diffusion coefficient is a non-monotonic function of temperature in the underdamped regime.However,when the external noise is present with a small intensity,the diffusion coefficient becomes a monotonically decreasing function of low temperatures.When the internal and external noise intensities are small,the average squared displacement of the particles as a function of time shows four different diffusion processes: thermalization,rapid normal diffusion,collapse and asymptotic recovery.These can be explained by the locked to running transition of the particles.In the second part,it is found through numerical simulation that the diffusion coefficient is a non-monotonic function of the correlation time of the internal OU noise when the bias force does not exist.this is explained as the resonance caused by the noise-induced frequency coupling with the potential well bottom frequency.When the bias force is added,the original resonance is destroyed by the bias force when it is larger than the restoring force,so that the non-monotonic relationship is replaced by a monotonically increasing function.The escape rate is a monotonically increasing function of the correlation time,which explains the result we obtained.When the bias force is small or absent,the diffusion coefficient is a negative power function of the damping coefficient,but a bias force that approximately corresponds to the extremum of the diffusion coefficient destroys this relationship,a "step" phenomenon appears in a small damping region.In the framework of the Kramers theory in spatial diffusion regime,we generalize the Kramers theory to finite potential barrier height.On the basis of the momentum of the particles in the potential well is limited,the barrier frequency at the top of the barrier is replaced by a non-local frequency and a parabolic approximation of the potential well and the barrier,we derive the stationary escape rate of the Brownian particles.The analytical results are in good agreement with the simulation results.The analytical results for diffusion coefficient are given when only single jump is taken in to account,which are in agreement with the simulation results.We develop an oscillation escape theory,and make a finite potential barrier height correction in spatial diffusion regime.The analytical results of the escape rate are in good agreement with the numerical simulation results,and the analytical results of the diffusion coefficient when only single jump is taken into account are in agreement with the simulation results,the small deviation can be attributed to long jump of the Brownian particles.