Nonlocal random walk over Floquet states of a dissipative nonlinear oscillator.

Abstract

We study transitions between the Floquet states of a periodically driven oscillator caused by the coupling of the oscillator to a thermal reservoir. The analysis refers to the oscillator that is driven close to triple its eigenfrequency and displays resonant period tripling. The interstate transitions result in a random "walk" over the states. We find the transition rates and show that the walk is nonlocal in the state space: the stationary distribution over the states is formed by the transitions between remote states. This is to be contrasted with systems in thermal equilibrium, where the distribution is usually formed by transitions between nearby states. The analysis of period tripling allows us to explore generic features of the dynamics of resonantly driven systems related to the multiplicity of the states, including those missing in the previously explored models of driven oscillators. We use the results to study switching between the period-3 states of the oscillator due to quantum fluctuations and find the scaling of the switching rates with the parameters.