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

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.

Strongly related to arXiV:0810.3251 (appeared in European Physical Journal B 61, 271 (2008)

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• Classical small systems coupled to finite baths
• Specific heat anomalies of small quantum systems subjected to finite baths
• Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: An exactly solvable non-dissipative non-ergodic model
• Nonergodic Brownian oscillator
• Ehrenfest approach to open double-well dynamics
• Correlations of correlations: Secondary autocorrelations in finite harmonic systems