Energy Barriers to Motion of Flux Lines in Random Media

TL;DR

This paper introduces algorithms to estimate energy barriers for flux line motion in 2D random media, confirming they scale similarly to free energy fluctuations through analytical and numerical evidence.

Contribution

It provides the first algorithms for bounding energy barriers and confirms their scaling behavior matches free energy fluctuations.

Findings

Bounds scale as t^{1/3} and t^{1/3}√ln t

Analytical and numerical support for barrier scaling

First confirmation of barrier and free energy fluctuation scaling equivalence

Abstract

We propose algorithms for determining both lower and upper bounds for the energy barriers encountered by a flux line in moving through a two-dimensional random potential. Analytical arguments, supported by numerical simulations, suggest that these bounds scale with the length $t$ of the line as $t^{1/3}$ and $t^{1/3}\sqrt{\ln t}$, respectively. This provides the first confirmation of the hypothesis that barriers have the same scaling as the fluctuation in the free energy. \pacs{PACS numbers: 74.60.Ge, 05.70.Ln, 05.40.+j}