An alternative, dynamic density functional-like theory for time-dependent density fluctuations in glass-forming fluids

Abstract

We propose an alternative theory for the relaxation of density fluctuations in glass-forming fluids. We derive an equation of motion for the density correlation function which is local in time and is similar in spirit to the equation of motion for the average non-uniform density profile derived within the dynamic density functional theory. We identify the Franz-Parisi free energy functional as the non-equilibrium free energy for the evolution of the density correlation function. An appearance of a local minimum of this functional leads to a dynamic arrest. Thus, the ergodicity breaking transition predicted by our theory coincides with the dynamic transition of the static approach based on the same non-equilibrium free energy functional.

accepted for publication in J. Chem. Phys. (Communication) Special Topic on Slow Dynamics

References in corpus (8)

• Theoretical perspective on the glass transition and amorphous materials
• Classical dynamical density functional theory: from fundamentals to applications
• Exact theory of dense amorphous hard spheres in high dimension. I. The free energy
• Glass transition of hard spheres in high dimensions
• Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids
• Long-wavelength fluctuations lead to a model of the glass crossover
• Systematic expansion in the order parameter for replica theory of the dynamical glass transition
• On the dynamics of Kac $p$-spin glasses