Newtonian Kinetic Theory and the Ergodic-Nonergodic Transition

TL;DR

This paper develops a field-theoretic approach to Newtonian kinetic theory to analyze ergodic-nonergodic transitions in dense fluids, revealing that low-frequency dynamics near the transition are similar for both Newtonian and Smoluchowski systems.

Contribution

It introduces a perturbation theory framework for Newtonian kinetic theory to study ENE transitions, showing equivalence in low-frequency dynamics for different microscopic dynamics.

Findings

Low-frequency dynamics near ENE transition are the same for Newtonian and Smoluchowski dynamics.

The developed theory provides a self-consistent model for studying ENE transitions.

Despite differences in density expansion, the dynamics converge at low frequencies.

Abstract

In a recent work we have discussed how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. In the present work we use this development for investigating ergodic-nonergodic (ENE) transitions in dense fluids. The theory is developed in terms of a core problem spanned by the variables $\rho$, the number density, and $B$, a response density. We set up the perturbation theory expansion for studying the self-consistent model which gives rise to a ENE transition. Our main result is that the low-frequency dynamics near the ENE transition is the same for Smoluchowski and Newtonian dynamics. This is true despite the fact that term by term in a density expansion the results for the two dynamics are fundamentally different.