Particle current statistics in driven mesoscale conductors

Abstract

We propose a highly scalable method to compute the statistics of charge transfer in driven conductors. The framework can be applied in situations of nonzero temperature, strong coupling to terminals, and in the presence of nonperiodic light-matter interactions, away from equilibrium. The approach combines the so-called mesoscopic leads formalism with full counting statistics. It results in a generalized quantum master equation that dictates the dynamics of current fluctuations and higher order moments of the probability distribution function of charge exchange. For generic time-dependent quadratic Hamiltonians, we provide closed-form expressions for computing noise in the nonperturbative regime of the parameters of the system, reservoir, or system-reservoir interactions. Having access to the full dynamics of the current and its noise, the method allows us to compute the variance of charge transfer over time in nonequilibrium configurations. The dynamics reveal that in driven systems, the average noise should be defined operationally with care over which period of time is covered.