Decoherence Sturdy Memories in the Presence of Quantum Dissipation

We consider N identical oscillators coupled to a single environment and show that the conditions for the existence of decoherence free subspaces are degeneracy of the oscillator frequencies and separability of the coupling with the environment. A formal exact equation for the evolution in the case of two oscillators is found and the decoherence free subspace is explicitly determined. A full analytical solution for any initial condition and general parameters (frequencies and dissipation constants) is given in the markovian approximation and zero temperature. We find that slight relaxation of degeneracy and separability conditions leads to the appearence of two components in the dynamical evolution with very different decoherence times. The ratio between the characteristic time of the weak and strong decoherent components is given by $\tau_{WD}/\tau_{SD}\approx k/\delta k$, where $\delta k$ is a measure of the nonseparability of the coupling to the environment and $k$ is the mean decay constant of the oscillators.