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In this paper we analyze the double Caldeira-Leggett model: the path integralapproach to two interacting dissipative harmonic oscillators. Assuming ageneral form of the interaction between the oscillators, we consider twodifferent situations: i) when each oscillator is coupled to its own reservoir,and ii) when both oscillators are coupled to a common reservoir. After derivingand solving the master equation for each case, we analyze the decoherenceprocess of particular entanglements in the positional space of bothoscillators. To analyze the decoherence mechanism we have derived a generaldecay function for the off-diagonal peaks of the density matrix, which appliesboth to a common and separate reservoirs. We have also identified the expectedinteraction between the two dissipative oscillators induced by their commonreservoir. Such reservoir-induced interaction, which gives rise to interestingcollective damping effects, such as the emergence of relaxation- anddecoherence-free subspaces, is shown to be blurred by the high-temperatureregime considered in this study. However, we find that different interactionsbetween the dissipative oscillators, described by rotating or counter-rotatingterms, result in different decay rates for the interference terms of thedensity matrix.

The double Caldeira-Leggett model: Derivation and solutions of the master equations, reservoir-induced interactions and decoherence