Non-equilibrium quantum transport coefficients and the transient dynamics of full counting statistics in the strong coupling and non-Markovian regimes

Non-equilibrium transport properties of quantum systems have recently become experimentally accessible in a number of platforms in so-called full-counting experiments that measure transient and steady state non-equilibrium transport dynamics. We show that the effect of the measurement back-action can be exploited to gain access to relevant transport coefficients. This relationship is general, but becomes most conspicuous in the transient dynamics of open quantum systems understrong coupling to non-Markovian environments. In order to explore this regime, a new simulation method for the generation of full counting statistics of non-Markovian, strong-coupling transport settings has been developed that is expressed in terms of a hierarchy of equations of motion. With this tool we gain access to the relevant regime and instantiate our proposal with the study of energetic conductance between two baths connected via a few level system.