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

## TL;DR

This paper investigates how a dissipative nonlinear oscillator driven near triple its eigenfrequency exhibits nonlocal transitions between Floquet states, leading to a random walk in state space and unique Floquet dynamics features.

## Contribution

It introduces a model of nonlocal Floquet state transitions in a driven oscillator, revealing new insights into multi-state Floquet dynamics and quantum switching behavior.

## Key findings

- Transition rates for Floquet states are derived.
- The stationary distribution involves remote state transitions.
- Switching rates scale with system parameters.

## 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 the features of the multi-state Floquet dynamics including those missing in the previously explored models of driven oscillators such as the absence of detailed balance for low temperatures. 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.