Study On Spontaneous Symmetry Breaking In Bidirectional Two-channel Asymmetric Simple Exclusion Process

In the natural world, there is a wide variety of material movement. Such as vehicular traffic systems in cities, the movement of molecular motors in vivo. In the course of these campaigns, the most common and most simple is one-dimensional movement. In the sixties and seventies of last century, there is a one-dimensional kinetic theory models have been proposed to simulate the dynamics of biopolymers mechanism, this model is the ASEP (asymmetric simple exclusion processes) model. ASEP model describes a one-dimensional system composed of a lattice string containing N and some particles, particle move in the lattice string, particles in the original grid can jump to both sides of the grid with a certain probability, but in the ASEP model, a grid can hold only one particle, therefore, the particles can not jump into the grid occupied by particle. If the probability of particle sports to one direction is 0, and only to the other direction, then we call it TASEP mosel(totally asymmetric simple exclusion processes), as TASEP model is more realistic movement, TASEP model has been more attention. Later, scientists have proposed a variety of extended model of TASEP model to describe more complex movement. In the study of the extends model of TASEP model,emergence a variety of cooperative phenomena which lots one-dimensional equilibrium systems do not. One of them is the spontaneous symmetry breaking.In chapter 2, we studies a two-lane totally asymmetric simple exclusion processes(TASEP) with narrow entrances under parallel and random update.Particles move on two parallel lanes in the opposite directions without changing. The narrow entrances are modeled in this way: the entry of a particle is not allowed if the exit site of the other lane is occupied (see also Pronina and Kolomeisky2007 J. Phys. A: Math. Theory. 40 2275). We mainly focus on the case where particles hop deterministically in the bulk. The phase diagram, bulk density and particle currents are analyzed using mean-field approximation. It is shown that there are two symmetry breaking phases, and one of them (i.e., asymmetric low density/low density phase) occupies only a line in the phase diagram when p =1,but when p <1,this case will appear by a phase. From Monte Carlo simulation results,we find that the simulation results deviate from the mean-field prediction obviously, because correlations are not considered in mean-field calculation. The phase diagram are reported in this chapter and can find that the introduction of stochastic hopping changes the phase diagram structure. In chapter 3, to solving the inconsistenty of the Monte Carlo simulation and mean field theory analysis of the front chapter, we present an improved mean field analysis of a bidirectional two-lane asymmetric exclusion processes with narrow entrances, which exhibits pontaneous symmetry breaking [Pronina and Kolomeisky, J.Phys.A 40, 2275 (2007)]. The improved mean field method takes into account the correlation of the vertical cluster at the system boundaries, which shows better agreement with simulation results than the simple mean field method.In chapter 4, we studies a two-lane totally asymmetric simple exclusion processes(TASEP) with narrow exports. The narrow exports are modeled in this way: the out of a particle is not allowed if the entrance site of the other lane is occupied. We use a simple mean field theory, the improved mean field theory and Monte Carlo simulation three methods to solve the model, the results show that the improved mean field theory much closer to the Monte Carlo simulation results than the simple mean field theory, and compared with the simple mean field theory, the improved mean field theory can be used narrower range.