Analytical And Simulation Studies On Complex Phase Transitions In Non-Equilibrium Multi-Particle Systems

Non-equilibrium systems are systems that develop away from equilibrium gradually as time changes.And they exists widely in nature and our daily life.To understand the basic properties of non-equilibrium systems,many paradigmatic models have been proposed,for example,the cellular automaton model in vehicle traffic,the ASEP(Asymmetric Simple Exclusion Process)model in the kinetics of synthesis of proteins and traffic flow and so on.These models are good for understanding some complex phenomena in reality.However,these original models are needed to be improved in further researches.There are controversial reports about the existence of asymmetric low density(LD)/low density(LD)phase in the study of spontaneous symmetry breaking in the bidirectional two-lane asymmetric simple exclusion processes.In order to make this clear,we investigate the asymmetric exclusion processes in two-lane with narrow entrances under random and parallel updates in this paper.To determine the existence of the asymmetric LD/LD phase,we propose an improved mean field analysis method-N cluster mean field analysis and minimum current principle which means that the phase which has minimum current when many phases may exist under the same condition is stable.With the increase of N,the theoretical analysis results are more and more accurate.Under the random update,N is changed from 1 to 6,and the currents of asymmetric LD/LD are always not least,which means that the asymmetric LD/LD phase does not exist.The finding is the same under parallel update with the N changing from 1 to 7.And the controversy is settled.In this paper,we also study the phase diagrams of KLS(Katz-Lebowitz-Spohn)processes on lattices with a junction,where particles move on parallel lattice branches that combine into a single lattice at the junction.In this investigation,Monte Carlo simulation and simple mean field analysis are used.And in simple mean field analysis,the system is mapped into three subsystems.With extremal current principle and flow rate conservation,we find that the analysis results are in excellent agreement with the simulation results.And the conditions of existence of some phases are also obtained with the change of parameters ? and ?.