Theoretical Studies On Non-equilibrium Statistical Problems In Self-propelled Particle Systems

In recent years,self-propelled particles(S(?)Ps),also known as active particles,have been an important research area in physics,chemistry,engineering and biology.Self-propelled particles have the ability to transfer the energy from environment or them-selves to their kinetic energy,and then drive the system out of equilibrium.Due to this property,they show a series of novel features,not only the single particle motions,but lots of collective behaviours.At present,the related research in this field is mainly focus on experiments and computer simulations,while the theoretical research is rela-tively few,and it is difficult and challenging.In this thesis,we focus on two class of collective behaviours,glass transition at high densities and active bath.We mainly use the non-equilibrium statistical mechanics methods to study those physical problems,also use some computer simulations.(1)Mode-coupling theory study of glass transition for self-propelled particles.From the basic theory in non-equilibrium statistical mechanics,we derived a mode-coupling theory(MCT)for self-propelled particles.The theory shows the glass transition of the system dependants on two important parameters,an averaged diffusion coefficient D and a non-trivial structural function S2(k),which are related with the activity of SSPs.The numerical results of MCT shows the critical glass transition density ρC increases with the increasing of activity v0,but decreases with the persistent time τp when the effective temperature Teff is constant.These results are confirmed with previous sim-ulations.We also extend our theory to a mixing system consisting of active particles and passive particles.Results show that the critical glass transition packing fraction ηC increases with the active particle component non-linearly.Furthermore we developed a theory to study the inertial effect on glass transition of SPPs.The theory shows the mass of the particles clearly change the glass transition behaviour of SPPs,which is strongly different with the equilibrium situations.(2)Statistical properties of active bathIn this thesis,we use theoretical methods to study the behaviour of a tracer im-mersed in active bath.Firstly,the mean-field theory is introduced to deal with the active particles and gives a evolution equation for density fluctuations of bath particles.Then we establish a generalized Langevin equation to study the effective transport properties of the tracer,such as diffusion and mobility.At last we discuss the effective temperature of the tracer in active bath.All results are confirmed with simulations.These results help us to understand more about the statistical properties of active bath.