Abstract
In this paper we study the four-point correlation function χ(4) of collective density fluctuations in a nonequilibrium liquid. The equilibration is controlled by a modified stretched exponential behavior (exp[-(t(w)/τ)(β)]) having the relaxation time τ dependent on the aging time t(w). Similar aging behavior has been seen experimentally in supercooled liquids. The basic equations of fluctuating nonlinear hydrodynamics are solved here numerically to obtain χ(4) 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.
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