Theory of relaxation and pumping of quantum oscillator non-resonantly coupled with the other oscillator

The paper shows mechanisms of both the pumping and energy decay of an 'isolated' oscillator. The oscillator is only coupled non-resonantly with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the 'isolated' oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian. The original model is reduced to two 'independent' open systems, with each containing original oscillators connected with their effective independent thermal baths, whose parameters are determined. The paper also gives a description of the obtained model in terms of quantum stochastic differential equations.