Noise-induced switching from a symmetry-protected shallow metastable state

TL;DR

This paper investigates how noise causes escape from a shallow, symmetry-protected metastable state in a nonlinear oscillator driven near triple its eigenfrequency, revealing how escape rates depend on system parameters.

Contribution

It provides a detailed analysis of escape rates from a symmetry-protected metastable state in a driven nonlinear oscillator, highlighting the scaling behavior and implications for mesoscopic systems.

Findings

Escape rate scales exponentially with system parameters.

Zero-amplitude state remains stable despite increased driving.

Fluctuations can spontaneously break time-translation symmetry.

Abstract

We consider escape from a metastable state of a nonlinear oscillator driven close to triple its eigenfrequency. The oscillator can have three stable states of period-3 vibrations and a zero-amplitude state. Because of the symmetry of period-tripling, the zero-amplitude state remains stable as the driving increases. However, it becomes shallow in the sense that the rate of escape from this state exponentially increases, while the system still lacks detailed balance. We find the escape rate and show how it scales with the parameters of the oscillator and the driving. The results facilitate using nanomechanical, Josephson-junction based, and other mesoscopic vibrational systems for studying, in a well-controlled setting, the rates of rare events in systems lacking detailed balance. They also describe how fluctuations spontaneously break the time-translation symmetry of a driven oscillator.