In this paper we analyze the double Caldeira-Leggett model: the path integral
approach to two interacting dissipative harmonic oscillators. Assuming a
general form of the interaction between the oscillators, we consider two
different situations: i) when each oscillator is coupled to its own reservoir,
and ii) when both oscillators are coupled to a common reservoir. After deriving
and solving the master equation for each case, we analyze the decoherence
process of particular entanglements in the positional space of both
oscillators. To analyze the decoherence mechanism we have derived a general
decay function for the off-diagonal peaks of the density matrix, which applies
both to a common and separate reservoirs. We have also identified the expected
interaction between the two dissipative oscillators induced by their common
reservoir. Such reservoir-induced interaction, which gives rise to interesting
collective damping effects, such as the emergence of relaxation- and
decoherence-free subspaces, is shown to be blurred by the high-temperature
regime considered in this study. However, we find that different interactions
between the dissipative oscillators, described by rotating or counter-rotating
terms, result in different decay rates for the interference terms of the
density matrix.Comment: 42 pages, 7 figures, new discussion added, typos adde
