Microscopic theory for the glass transition in a system without static correlations

TL;DR

This paper develops a microscopic theory predicting a glass transition in a system of hard rods without static correlations, based on the dynamics of orientational motion and torque-torque correlations.

Contribution

It introduces a novel theoretical framework that predicts a glass transition solely from dynamic correlations, without relying on static structural correlations.

Findings

Predicts a glass transition at a critical rod length l_c

Shows the diffusion constant vanishes as (l_c - l)^b with b=1 near the transition

Demonstrates the transition occurs without static correlations, unlike mode coupling theory

Abstract

We study the orientational dynamics of infinitely thin hard rods of length L, with the centers-of-mass fixed on a simple cubic lattice with lattice constant a.We approximate the influence of the surrounding rods onto dynamics of a pair of rods by introducing an effective rotational diffusion constant D(l),l=L/a. We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a time-dependent torque-torque correlator of an isolated pair of rods. A glass transition occurs at l_c, if v(l_c)=1. We present a variational and a numerically exact evaluation of v(l).Close to l_c the diffusion constant decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a glass transition in the absence of any static correlations, in contrast to present form of mode coupling theory.