Parametric resonance for enhancing the rate of metastable transition

TL;DR

This paper develops a theoretical framework to quantify how periodic parametric excitation at resonant frequencies can significantly increase the rate of metastable transitions in high-dimensional stochastic systems, with applications to material defect healing.

Contribution

It introduces a higher-order Hamiltonian formalism and perturbation analysis for the Freidlin-Wentzell action functional applicable to complex kinetic Langevin systems, providing explicit rate change formulas.

Findings

Resonant parametric excitation can greatly enhance transition rates.

The theory applies to high-dimensional, nonlinear stochastic systems.

Numerical experiments confirm the effectiveness in molecular models.

Abstract

This work is devoted to quantifying how periodic perturbation can change the rate of metastable transition in stochastic mechanical systems with weak noises. A closed-form explicit expression for approximating the rate change is provided, and the corresponding transition mechanism can also be approximated. Unlike the majority of existing relevant works, these results apply to kinetic Langevin equations with high-dimensional potentials and nonlinear perturbations. They are obtained based on a higher-order Hamiltonian formalism and perturbation analysis for the Freidlin-Wentzell action functional. This tool allowed us to show that parametric excitation at a resonant frequency can significantly enhance the rate of metastable transitions. Numerical experiments for both low-dimensional toy models and a molecular cluster are also provided. For the latter, we show that vibrating a material appropriately can help heal its defect, and our theory provides the appropriate vibration.