A generalized fidelity amplitude for open systems

We consider a central system which is coupled via dephasing to an open system, i.e. an intermediate system which in turn is coupled to another environment. Considering intermediate and far environment as one composite system, the coherences in the central system are given in the form of fidelity amplitudes for a certain perturbed echo dynamics in the composite environment. On the basis of the Born-Markov approximation, we derive a master equation for the reduction of that dynamics to the intermediate system alone. In distinction to an earlier paper [arXiv: 1502.04143 (2015)] where we discussed the stabilizing effect of the far environment on the decoherence in the central system, we focus here on the possibility to use the measurable coherences in the central system for probing the open quantum dynamics in the intermediate system. We illustrate our results for the case of chaotic dynamics in the near environment, where we compare random matrix simulations with our analytical result.