Noisy classical field theories with two coupled fields: Dependence of escape rates on relative field stiffness

Abstract

Exit times for stochastic Ginzburg-Landau classical field theories with two or more coupled classical fields depend on the interval length on which the fields are defined, the potential in which the fields deterministically evolve, and the relative stiffness of the fields themselves. The latter is of particular importance in that physical applications will generally require different relative stiffnesses, but the effect of varying field stiffnesses has not heretofore been studied. In this paper, we explore the complete phase diagram of escape times as they depend on the various problem parameters. In addition to finding a transition in escape rates as the relative stiffness varies, we also observe a critical slowing down of the string method algorithm as criticality is approached.

A Bifurcation Monte Carlo Scheme for Rare Event Simulation

“…Much theoretical and computational work has gone into this rare-event problem [15] [16] [17] [18]. The theoretical estimate of the transition rate is the Kramers (or Van't Hoff-Arrhenius) law,…”

Lifetimes of metal nanowires with broken axial symmetry

“…As discussed in [15] and [16], the time evolution of the fields under noise can be described by the coupled Langevin equations˙…”

“…In particular, we consider here quadrupolar deformations of the nanowire cross-section, which cost less surface energy than higher-multipole deformations, and were shown to be the most common stable deformations within linear stability analyses [11,14]. The general mathematical treatment of such problems was discussed in [15,16]. Of particular interest was the discovery of a transition in activation behavior not only as wire length varies [12], but also as bending coefficients for the two fields vary [16].…”

“…In particular, we consider here quadrupolar deformations of the nanowire cross-section, which cost less surface energy than higher-multipole deformations, and were shown to be the most common stable deformations within linear stability analyses [11,14]. The general mathematical treatment of such problems was discussed in [15,16]. Of particular interest was the discovery of a transition in activation behavior not only as wire length varies [12], but also as bending coefficients for the two fields vary [16].In this paper, we use these results and those of Urban et al [9,11] to construct a more general theory of lifetimes of nanowires with both axisymmetric and nonaxisymmetric cross-sections, as functions of temperature, strain, and other thermodynamic variables.…”

“…The general mathematical treatment of such problems was discussed in [15,16]. Of particular interest was the discovery of a transition in activation behavior not only as wire length varies [12], but also as bending coefficients for the two fields vary [16].In this paper, we use these results and those of Urban et al [9,11] to construct a more general theory of lifetimes of nanowires with both axisymmetric and nonaxisymmetric cross-sections, as functions of temperature, strain, and other thermodynamic variables.…”