Dissipative corrections to escape probabilities of thermal-nonequilibrium systems

Period Tripling due to Parametric Down-Conversion in Circuit QED

Discrete time-translation symmetry breaking can be observed in periodically driven systems oscillating at a fraction of the frequency of the driving force. However, with the exception of the parametric instability in period doubling, multiperiodic driving does not lead to an instability threshold. In this Letter, we point out that quantum vacuum fluctuations can be generically employed to induce period multiplication. In particular, we discuss the period-tripled states in circuit QED and propose a microwave setup. We show that for weak dissipation or strong driving, the system exhibits a nonequilibrium phase transition in the sense that the timescale over which the period-tripled state is generated can be arbitrarily separated from the timescale of the subsequent dephasing.

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

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.

Noise induced escape from a nonhyperbolic chaotic attractor of a periodically driven nonlinear oscillator

Noise induced escape from the domain of attraction of a nonhyperbolic chaotic attractor in a periodically excited nonlinear oscillator is investigated. The general mechanism of the escape in the weak noise limit is studied in the continuous case, and the fluctuational path is obtained by statistical analysis. Selecting the primary homoclinic tangency as the initial condition, the action plot is presented by parametrizing the set of escape trajectories and the global minimum gives rise to the optimal path. Results of both methods show good agreements. The entire process of escape is discussed in detail step by step using the fluctuational force. A structure of hierarchical heteroclinic crossings of stable and unstable manifolds of saddle cycles is found, and the escape is observed to take place through successive jumps through this deterministic hierarchical structure.