Periodic thermodynamics of the parametrically driven harmonic oscillator

TL;DR

This paper analyzes the quasistationary distribution of a parametrically driven harmonic oscillator coupled to a thermal bath, revealing how its effective quasitemperature can be manipulated through spectral density design, with implications for quasithermal control.

Contribution

It derives the quasistationary Floquet-state occupation probabilities and demonstrates quasithermal engineering by spectral density design, including effective cooling and quasithermal instability.

Findings

Quasistationary distribution follows a geometrical Boltzmann form.

Quasitemperature can be tuned independently of bath temperature.

Quasithermal instability can occur in mechanically stable systems.

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.