Coupled quantum oscillators within independent quantum reservoirs

TL;DR

This paper derives and analyzes the quantum Langevin equations for two coupled oscillators in separate heat baths, revealing nonmonotonic interaction energy dependence and effects of temperature differences.

Contribution

It introduces a model Hamiltonian and Heisenberg equations to analyze coupled quantum oscillators in independent reservoirs, highlighting nontrivial energy interactions.

Findings

Interaction energy shows nonmonotonic dependence on coupling strength.

Temperature differences between heat baths significantly affect energy quantities.

Derived expressions for mean energies of oscillators and their interaction.

Abstract

System of the quantum Langevin equations for two quantum coupling oscillators within independent heat baths of quantum oscillators are obtained using a model Hamiltonian and corresponding Heisenberg equations of motion. Expressions for mean energy of coupled oscillators and their mean energy of interaction are derived and analyzed. Nonmonotonic dependence of the interaction energy versus a coupling constant is demonstrated and explained. Nontrivial dependence of the quantities as a consequence of the difference in temperatures of heat baths is shown.