Anomalous Size Dependence of Relaxational Processes

TL;DR

This paper investigates how the size of a system influences relaxation processes that follow stretched exponential behavior, revealing a size-dependent crossover to simple exponential decay above a certain time.

Contribution

It introduces a model showing size-dependent relaxation crossover in systems with competing exponential processes, relevant for simulations and experiments.

Findings

Relaxation changes from stretched exponential to simple exponential after a size-dependent crossover time

Crossover time depends logarithmically on system size

Decay rate also depends logarithmically on system size

Abstract

We consider relaxation processes that exhibit a stretched exponential behavior. We find that in those systems, where the relaxation arises from two competing exponential processes, the size of the system may play a dominant role. Above a crossover time tx that depends logarithmically on the size of the system the relaxation changes from a stretched exponential to a simple exponential decay, where the decay rate also depends logarithmically on the size of the system. This result is relevant to large-scale Monte-Carlo simulations and should be amenable to experimental verification in low-dimensional and mesoscopic systems.