Nonequilibrium dynamics of four-point correlations of collective density fluctuations in a supercooled liquid

Abstract

In this paper we study the four-point correlation function χ₄ of collective density fluctuations in a nonequilibrium liquid. The equilibration is controlled by a modified stretched exponential behavior {exp[−(tw/τ)β]} having the relaxation time τ dependent on the aging time tw. Similar aging behavior has been seen experimentally in supercooled liquids. The basic equations of fluctuating nonlinear hydrodynamics are solved here numerically to obtain χ₄ for equilibrium and non equilibrium states. We also identify a dynamic length scale ξ from the equilibrated function. ξ(T) grows with fall of temperature T. From a broader perspective, we demonstrate here that the characteristic signatures of dynamical heterogeneities in a supercooled liquid, observed previously in computer simulations of the dynamics of a small number of particles, are also present in the coarse grained equations of generalized hydrodynamics.