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System of the quantum Langevin equations for two quantum coupling oscillatorswithin independent heat baths of quantum oscillators are obtained using a modelHamiltonian and corresponding Heisenberg equations of motion. Expressions formean energy of coupled oscillators and their mean energy of interaction arederived and analyzed. Nonmonotonic dependence of the interaction energy versusa coupling constant is demonstrated and explained. Nontrivial dependence of thequantities as a consequence of the difference in temperatures of heat baths isshown.

Coupled quantum oscillators within independent quantum reservoirs