Crossovers in the thermal decay of metastable states in discrete systems

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 saddle-point solution, with all degrees of freedom decaying instantly. Increasing the barrier one enters the elastic regime, where the decay is due to bent saddle-point 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 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.