Periodic thermodynamics of the parametrically driven harmonic oscillator

Abstract

We determine the quasistationary distribution of Floquet-state occupation probabilities for a parametrically driven harmonic oscillator coupled to a thermal bath. Since the system exhibits detailed balance, and the canonical representatives of its quasienergies are equidistant, these probabilities are given by a geometrical Boltzmann distribution, but its quasitemperature differs from the actual temperature of the bath, being affected by the functional form of the latter's spectral density. We provide two examples of quasithermal engineering, i.e., of deliberate manipulation of the quasistationary distribution by suitable design of the spectral density: We show that the driven system can effectively be made colder than the undriven one, and demonstrate that quasithermal instability can occur even when the system is mechanically stable.

arXiv comment13 pages, 11 figures

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• Periodic thermodynamics of the Rabi model with circular polarization for arbitrary spin quantum numbers
• Floquet-state cooling
• A framework for sequential measurements and general Jarzynski equations
• Theory of Non-equilibrium Asymptotic State Thermodynamics: Interacting Ehrenfest Urn Ring as an Example
• Periodic thermodynamics of a two spin Rabi model
• Environment-controlled Floquet-state paramagnetism