  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.
