Mode coupling theory for nonequilibrium glassy dynamics of thermal self-propelled particles

We present a mode coupling theory study for the relaxation and glassy dynamics of a system of strongly interacting self-propelled particles, wherein the self-propulsion force is described by Ornstein-Uhlenbeck colored noise and thermal noises are included. Our starting point is an effective Smoluchowski equation governing the distribution function of particle positions, from which we derive a memory function equation for the time dependence of density fluctuations in nonequilibrium steady states. With the basic assumption of the absence of macroscopic currents and standard mode coupling approximation, we can obtain expressions for the irreducible memory function and other relevant dynamic terms, wherein the nonequilibrium character of the active system is manifested through an averaged diffusion coefficient (D) over bar and a nontrivial structural function S-2(q) with q being the magnitude of wave vector q. (D) over bar and S-2(q) enter the frequency term and the vertex term for the memory function, and thus influence both the short time and the long time dynamics of the system. With these equations obtained, we study the glassy dynamics of this thermal self-propelled particle system by investigating the Debye-Waller factor f(q) and relaxation time tau(alpha) as functions of the persistence time tau(p) of self-propulsion, the single particle effective temperature T-eff as well as the number density p. Consequently, we find the critical density p(c) for given tau(p) shifts to larger values with increasing magnitude of propulsion force or effective temperature, in good accordance with previously reported simulation work. In addition, the theory facilitates us to study the critical effective temperature T-eff(c) for fixed p as well as its dependence on tau(p). We find that T-eff(c) increases with tau(p) and in the limit tau(p) -> 0, it approaches the value for a simple passive Brownian system as expected. Our theory also well recovers the results for passive systems and can be easily extended to more complex systems such as active-passive mixtures.