Equilibrium states of a test particle coupled to finite size heat baths

TL;DR

This paper uses numerical simulations to explore how a test particle interacts with finite heat baths, revealing spectral dependencies and frequency shifts affecting thermalization, with implications for nanomechanical systems.

Contribution

It demonstrates that thermalization depends on the spectral properties of finite heat baths and uncovers an unexpected frequency shift in the particle's response.

Findings

Thermalization is spectral-dependent, influenced by bath oscillator frequencies.

Presence of two heat baths constrains thermalization conditions.

Frequency shift observed in the test particle response relative to bath spectra.

Abstract

We report on numerical simulations of the dynamics of a test particle coupled to competing Boltzmann heat baths of finite size. After discussing some features of the single bath case, we show that the presence of two heat baths further constraints the conditions necessary for the test particle to thermalize with the heat baths. We find that thermalization is a spectral property in which the oscillators of the bath with frequencies in the range of the test particle characteristic frequency determine its degree of thermalization. We also find an unexpected frequency shift of the test particle response with respect to the spectra of the two heat baths. Finally, we discuss implications of our results for the study of high-frequency nanomechanical resonators through cold damping cooling techniques, and for engineering reservoirs capable of mitigating the back-action on a mechanical system.