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[combining macron] and a nontrivial structural function S(q) with q being the magnitude of wave vector q. D[combining macron] and S(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 and relaxation time τ as functions of the persistence time τ of self-propulsion, the single particle effective temperature T as well as the number density ρ. Consequently, we find the critical density ρ for given τ 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 for fixed ρ as well as its dependence on τ. We find that T increases with τ and in the limit τ → 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.

Collective behaviours of active particle systems have gained great research attentions in recent years. Here we present a mode-coupling theory (MCT) framework to study the glass transition of a mixture system of active and passive Brownian particles. The starting point is an effective Smoluchowski equation, which governs the dynamics of the probability distribution function in the position phase space. With the assumption of the existence of a nonequilibrium steady state, we are able to obtain dynamic equations for the intermediate scattering functions (ISFs), wherein an irreducible memory function is introduced which in turn can be written as functions of the ISFs based on standard mode-coupling approximations. The effect of particle activity is included through an effective diffusion coefficient which can be obtained via short time simulations. By calculating the long-time limit of the ISF, the Debye-Waller (DW) factor, one can determine the critical packing fraction η c of glass transition. We find that for active-passive (AP) mixtures with the same particle sizes, η c increases as the partial fraction of active particle x A increases, which is in agreement with previous simulation works. For system with different active/passive particle sizes, we find an interesting reentrance behaviour of glass transition, i.e., η c shows a non-monotonic dependence on x A. In addition, such a reentrance behaviour would disappear if the particle activity is large enough. Our results thus provide a useful theoretical scheme to study glass transition behaviour of active-passive mixture systems in a promising way.