Large Fluctuations, Classical Activation, Quantum Tunneling, and Phase Transitions

TL;DR

This paper unifies the understanding of phase transitions in stochastic escape problems across classical and quantum systems, revealing a mapping between them and analyzing critical behaviors in nanowires and magnetic systems.

Contribution

It introduces a unified theoretical framework linking classical and quantum escape problems and explores their critical transition behaviors.

Findings

Existence of a mapping between classical and quantum escape problems.

Identification of critical behavior at phase transitions in both classes.

Application to nanowire breakup and magnetization reversal.

Abstract

We study two broad classes of physically dissimilar problems, each corresponding to stochastically driven escape from a potential well. The first class, often used to model noise-induced order parameter reversal, comprises Ginzburg-Landau-type field theories defined on finite intervals, perturbed by thermal or other classical spatiotemporal noise. The second class comprises systems in which a single degree of freedom is perturbed by both thermal and quantum noise. Each class possesses a transition in its escape behavior, at a critical value of interval length and temperature, respectively. It is shown that there exists a mapping from one class of problems to the other, and that their respective transitions can be understood within a unified theoretical context. We consider two applications within the first class: thermally induced breakup of monovalent metallic nanowires, and stochastic reversal of magnetization in thin ferromagnetic annuli. Finally, we explore the depth of the analogy between the two classes of problems, and discuss to what extent each case exhibits the characteristic signs of critical behavior at a sharp second-order phase transition.