Periodically Driven Harmonic Langevin Systems

Abstract

Motivated to understand the asymptotic behavior of periodically driven thermodynamic systems, we study the prototypical example of Brownian particle, overdamped and underdamped, in harmonic potentials subjected to periodic driving. The harmonic strength and the coefficients of drift and diffusion are all taken to be $T$-periodic. We obtain the asymptotic distributions almost exactly treating driving nonperturbatively. In the underdamped case, we exploit the underlying $S{L}_2$ symmetry to obtain the asymptotic state, and study the dynamics and fluctuations of energies and entropy. We further obtain the two-time correlation functions, and investigate the responses to drift and diffusion perturbations in the presence of driving.

arXiv commentJournal version; added comments on nonperturbative treatment and the advantages of the method used, including an illustrative example; removed an erroneous statement and related comments that has no bearing on any equation

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Cited by in corpus (2)

• Oscillating states of periodically driven anharmonic Langevin systems
• Oscillating states of driven Langevin systems in large viscous regime