Strong non-exponential relaxation and memory effects in a fluid with non-linear drag

Abstract

We analyse the dynamical evolution of a fluid with non-linear drag, for which binary collisions are elastic, described at the kinetic level by the Enskog-Fokker-Planck equation. This model system, rooted in the theory of non-linear Brownian motion, displays a really complex behaviour when quenched to low temperatures. Its glassy response is controlled by a long-lived non-equilibrium state, independent of the degree of non-linearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behaviour persists in the collisionless case, where the fluid is described by the non-linear Fokker-Planck equation. The observed response, which includes non-exponential, algebraic, relaxation and strong memory effects, presents scaling properties: the time evolution of the temperature -- for both relaxation and memory effects -- falls onto a master curve, regardless of the details of the experiment. To account for the observed behaviour in simulations, it is necessary to develop an extended Sonine approximation for the kinetic equation -- which considers not only the fourth cumulant but also the sixth one.