Ergodicity and slow diffusion in a supercooled liquid

TL;DR

This paper models the slow dynamics of supercooled liquids using fluctuating nonlinear hydrodynamics, highlighting how compressibility and nonlinear couplings influence ergodicity and relaxation times.

Contribution

It introduces a modified FNH model including diffusive modes and nonlinearities, revealing their impact on ergodicity and relaxation in supercooled liquids.

Findings

Diffusive modes influence relaxation times in supercooled liquids.

Compressibility and nonlinear couplings are crucial for slow dynamics.

The model challenges the sharp ergodicity-nonergodicity transition prediction.

Abstract

A model for the slow dynamics of the supercooled liquid is formulated in terms of the standard equations of fluctuating nonlinear hydrodynamics (FNH) with the inclusion of an extra diffusive mode for the collective density fluctuations. If the compressible nature of the liquid is completely ignored, this diffusive mode sets the longest relaxation times in the supercooled state and smooths off a possible sharp ergodicity-nonergodicity (ENE) transition predicted in a mode coupling theory. The scenario changes when the complete dynamics is considered with the inclusion of $1/\rho$ nonlinearities in the FNH equations, reflecting the compressible nature of the liquid. The latter primarily determines the extent of slowing down in the supercooled liquid. The presence of slow diffusive modes in the supercooled liquid do not give rise to very long relaxation times unless the role of couplings between density and currents in the compressible liquid is negligible.