Slow dynamics due to entropic barriers in the one-dimensional `descent model'

TL;DR

This paper introduces a simple one-dimensional model demonstrating slow, aging dynamics caused by entropic barriers, with exact static solutions and an analytical evolution equation revealing logarithmic energy relaxation.

Contribution

The paper presents a novel one-dimensional model exhibiting aging and slow dynamics due to entropic barriers, with exact static solutions and an analytical description of the slow modes.

Findings

Model exhibits aging and slow relaxation at zero temperature.

Energy relaxes logarithmically as e(t) ~ 1/ln(t).

Exact solutions for static properties and dynamics are derived.

Abstract

We propose a novel one-dimensional simple model without disorder exhibiting slow dynamics and aging at the zero temperature limit. This slow dynamics is due to entropic barriers. We exactly solve the statics of the model. We derive an evolution equation for the slow modes of the dynamics which are responsible for the aging. This equation is equivalent to a random walker on the energetic landscape. This latter elementary model can be solved analytically up to some basic approximations and is eventually shown to present aging by itself, as well as a slow logarithmic relaxation of the energy: e(t) ~ 1/ln(t) at large t.