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Two-time correlations are a crucial tool to probe the dynamics of many-bodysystems. We use these correlation functions to study the dynamics ofdissipative quantum systems. Extending the adiabatic elimination method, weshow that the correlations can display two distinct behaviors, depending on theobservable of interest: a fast exponential decay, with a timescale of the orderof the dissipative coupling, or a much slower dynamics. We apply this formalismto bosons in a double well subjected to phase noise. While the single-particlecorrelations decay exponentially, the density-density correlations display slowaging dynamics. We also show that the two-time correlations of dissipativelyengineered quantum states can evolve in a drastically different manner comparedto their Hamiltonian counterparts.

Two-time Correlations Probing the Dynamics of Dissipative Many-Body Quantum Systems: Aging and Fast Relaxation