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.
Highlights
We consider escape from a metastable state of a nonlinear oscillator driven close to triple its eigenfrequency
One is the possibility to facilitate the comparison of the theory and the experiment on escape from a metastable state of a generic thermally nonequilibrium system in the presence of weak noise
The second is the spontaneous breaking of the time-translation symmetry in vibrational systems where the symmetry-preserving state is dynamically stable
Summary
We consider escape from a metastable state of a nonlinear oscillator driven close to triple its eigenfrequency. 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 describe how fluctuations spontaneously break the time-translation symmetry of a driven oscillator. A most detailed comparison of the theory and the experiment can be done for “shallow” metastable states These are states with a comparatively low barrier for escape. Even a comparatively weak noise can lead to escape from a shallow state with an appreciable rate. For stable states of forced vibrations such scaling has been found in the classical and quantum regimes[34,35,36] and has been observed both for the vibrations at the frequency of the driving resonant field[21,23,26,31,32] and for parametrically excited vibrations at half the drive frequency[22,24]
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