Crossovers in the thermal decay of metastable states in discrete systems

TL;DR

This paper analyzes how the thermal decay of metastable states in discrete chains transitions from rigid to elastic regimes, revealing boundary and bulk nucleation phenomena and providing decay rate calculations relevant to physical systems like Josephson lines.

Contribution

It introduces a detailed analysis of the crossover from rigid to elastic decay regimes in discrete systems, including boundary and bulk nucleation effects and decay rate computations.

Findings

Identification of a crossover from boundary to bulk nucleation within the elastic regime.

Decay rates computed in both regimes using Gaussian approximation and beyond steepest descent.

Scaling behavior of the prefactor near the rigid-to-elastic crossover.

Abstract

The thermal decay of linear chains from a metastable state is investigated. A crossover from rigid to elastic decay occurs when the number of particles, the single particle energy barrier or the coupling strength between the particles is varied. In the rigid regime, the single particle energy barrier is small compared to the coupling strength and the decay occurs via a uniform saddlepoint solution, with all degrees of freedom decaying instantly. Increasing the barrier one enters the elastic regime, where the decay is due to bent saddlepoint configurations using the elasticity of the chain to lower their activation energy. Close to the rigid-to-elastic crossover, nucleation occurs at the boundaries of the system. However, in large systems, a second crossover from boundary to bulk nucleation can be found within the elastic regime, when the single particle energy barrier is further increased. We compute the decay rate in the rigid and in the elastic regimes within the Gaussian approximation. Around the rigid-to-elastic crossover, the calculations are performed beyond the steepest descent approximation. In this region, the prefactor exhibits a scaling property. The theoretical results are discussed in the context of discrete Josephson transmission lines and pancake vortex stacks that are pinned by columnar defects.