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

Abstract

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.

Mode-Coupling Theory of the Glass Transition: A Primer

“…It was found that the critical density at which the glass transition takes place shifts to larger values with increasing magnitude of the self-propulsion force or effective temperature, and that the critical effective glass temperature increases with the persistence time. In the limit of a vanishing persistence time, the theory naturally yields the expected result for a simple passive Brownian system [95].…”

Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles

“…The nonequilibrium nature of the system is manifested through a time-dependent effective temperature, T ef f (τ ), derived from a generalized FDR. This shows that description of such systems within a mode-coupling theoretical framework in terms of the correlation function alone [17,24,28] is incomplete. T ef f (τ ) has two distinct regimes: at very short times (τ ≪ τ p ) we have T ef f (τ ) = T and it dynamically evolves to a higher value, determined by the parameters of activity, at long time (τ ≫ τ p ).…”

Active glasses

“…An MCT-based scaling analysis for this type of active-matter system was later performed by Nandi and Gov [165]. Feng and Hou subsequently studied a thermal version of the active Ornstein-Uhlenbeck model that also includes thermal translational noise [109]. Their MCT derivation differs fundamentally from the approach taken by Szamel [164], however: it is valid only for sufficiently small persistence times and does not require explicit velocity correlations as input.…”