Periodically driven harmonic Langevin systems

Oscillating states of driven Langevin systems under large viscous drives

We provide a perturbative scheme that is suitable to study oscillating states in driven Langevin systems in the large viscous regime. We explicitly determine the oscillating state distribution of an underdamped Brownian particle driven by a time-dependent periodic potential. Apart from the harmonic and anharmonic parameters of the potential, the noise strength and the viscous parameter (or equivalently their ratio referred to as the thermal parameter), which appear in the dynamics of the Brownian particle, are also driven periodically. We specify various nonequilibrium observables, relevant to characterize the oscillating states, and evaluate them to linear order in anharmonic perturbation. We find that the effect of viscous drives on oscillating states is measurable even at leading order and show that the thermodynamic properties of the system in these states are significantly distinct from those in equilibrium or even from those exhibited by oscillating states of overdamped driven systems.

Oscillating states of periodically driven anharmonic Langevin systems

We investigate the asymptotic distributions of periodically driven anharmonic Langevin systems. Utilizing the underlying SL_{2} symmetry of the Langevin dynamics, we develop a perturbative scheme in which the effect of periodic driving can be treated nonperturbatively to any order of perturbation in anharmonicity. We spell out the conditions under which the asymptotic distributions exist and are periodic and show that the distributions can be determined exactly in terms of the solutions of the associated Hill equations. We further find that the oscillating states of these driven systems are stable against anharmonic perturbations.