Current fluctuations in a dissipative environment

We have recently developed methods for calculating the statistics of a single counted quantity in a stochastic transport process described by a non-Markovian generalized master equation. Here, we expand on these ideas and extend our formalism to several counted quantities, allowing us to study cross-correlations between different variables. As an illustrative example, we consider charge transport through a double quantum dot capacitively coupled to a quantum point contact. We calculate the cross-correlations between the current through the double quantum dot and the current through the quantum point contact, and demonstrate the sensitivity of this cross-correlator to measurement quantum back-action.