Langevin dynamics of the glass forming polymer melt: fluctuations around the random phase approximation

TL;DR

This paper develops a theoretical framework using the Martin-Siggia-Rose formalism to analyze Langevin dynamics in glass-forming polymer melts, accounting for fluctuations beyond the random phase approximation and exploring implications for the glass transition.

Contribution

It introduces a method to incorporate fluctuations around RPA in Langevin dynamics of polymers, including cases where the fluctuation-dissipation theorem is violated.

Findings

Derived equations for correlation and response functions including fluctuations

Showed FDT holds leads to Mori-Zwanzig-like equations

Linked the memory kernel to mode-coupling theory

Abstract

In this paper the Martin-Siggia-Rose (MSR) functional integral representation is used for the study of the Langevin dynamics of a polymer melt in terms of collective variables: mass density and response field density. The resulting generating functional (GF) takes into account fluctuations around the random phase approximation (RPA) up to an arbitrary order. The set of equations for the correlation and response functions is derived. It is generally shown that for cases whenever the fluctuation-dissipation theorem (FDT) holds we arrive at equations similar to those derived by Mori-Zwanzig. The case when FDT in the glassy phase is violated is also qualitatively considered and it is shown that this results in a smearing out of the ideal glass transition. The memory kernel is specified for the ideal glass transition as a sum of all water-melon diagrams. For the Gaussian chain model the explicit expression for the memory kernel was obtained and discussed in a qualitative link to the mode-coupling equation.