Mode Coupling Theory for Nonequilibrium Glassy Dynamics of Thermal Self-Propelled Particles

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We present a promising 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's 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 absence of macroscopic currents and standard mode coupling approximation, we can obtain expressions for the irreducible memory function and other relevant dynamic terms. With these equations obtained, we study the glassy dynamics of this thermal self-propelled particles system by investigating the Debye-Waller factor fq and relaxation time τα as functions of the persistence time τₚ of self-propulsion, the single particle effective temperature Teff as well as the number density ρ. Consequently, we find the critical density ρc for given τₚ shifts to larger values with increasing magnitude of propulsion force or effective temperature, in good accordance with previous reported simulation works. In addition, the theory facilitates us to study the critical effective temperature Teffᶜ for fixed ρas well as its dependence on τₚ. We find that Teffᶜ increases with τₚ and in the limit τₚ→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.