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

Area of Science:

• Nonlinear dynamics
• Statistical physics
• Complex systems

Background:

• Metastable states in nonlinear oscillators are crucial for understanding complex system dynamics.
• Driven systems, especially near resonance, exhibit rich phenomena like period-tripling.
• Detailed balance is a common assumption, but many real-world systems lack it.

Purpose of the Study:

• To analyze the escape rate from a metastable zero-amplitude state in a nonlinear oscillator driven near its triple eigenfrequency.
• To investigate the scaling of this escape rate with system parameters.
• To explore spontaneous symmetry breaking in driven systems.

Main Methods:

• Theoretical analysis of a nonlinear oscillator model.
• Calculation of escape rates from a metastable state.
• Examination of system behavior near resonance and in the absence of detailed balance.

Main Results:

• The zero-amplitude state remains stable but becomes shallow as driving increases.
• Escape rate increases exponentially with driving, even in systems lacking detailed balance.
• The study derives the scaling of the escape rate with oscillator and driving parameters.

Conclusions:

• The findings provide a framework for studying rare event rates in systems without detailed balance.
• This research facilitates controlled experiments using mesoscopic systems like nanomechanical and Josephson-junction devices.
• The study demonstrates how fluctuations can spontaneously break time-translation symmetry in driven oscillators.