| The establishment of Langevin equation and Fokker-Planck equation provide base for people to study Brownian motion. Most problems can be modeled as Brownian motion. The resolution of the Fokker-Planck equation is very difficult. At present, only free field, linear potential and harmonic potential can be solved exactly. In most cases, we have to get the approximate analytic or numerical solution. Equivalent nonlinear system method is an effective method, but there is still larger error. The influence of stochastic force on non-equilibrium phase transition, especially the noise-induced phase transition is an important topic. The mean field method is the main method to study the non-equilibrium phase transition. We study a zero-dimen- sional system of Brownian particles which move in a periodic potential and subjected to an internal time derivative Ornstein-Uhlenbeck noise. We use the equivalent system method to get the approximate analytical solution. Then, we discuss the noise-induced phase transition problem and the influence of the potential shape, obtain the following conclusions: The new criteria improves the accuracy of the approximate analytical solution; phase transition mainly depends on the height of the potential barrier but insensitive to the shape of the potential. At last we study the phase point changes with noise correlation time, we find: when correlation time is small, phase point lies in low potential barrier height, conversely phase point lies in high potential barrier height. We then analyse the physical mechanism of phase transition. |
