Particle current statistics in driven mesoscale conductors

TL;DR

This paper introduces a scalable method combining mesoscopic leads formalism with full counting statistics to analyze charge transfer fluctuations in driven mesoscopic conductors under various non-equilibrium conditions.

Contribution

It presents a generalised quantum master equation framework for calculating current fluctuations and higher moments in time-dependent quadratic Hamiltonian systems, applicable beyond perturbative regimes.

Findings

Provides closed-form expressions for noise in non-perturbative regimes.

Enables computation of charge transfer variance in non-equilibrium.

Highlights the importance of operational definitions of noise in driven systems.

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 non-zero temperature, strong coupling to terminals and in the presence of non-periodic light-matter interactions, away from equilibrium. The approach combines the so-called mesoscopic leads formalism with full counting statistics. It results in a generalised 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 non-perturbative 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 non-equilibrium configurations. The dynamics reveal that in driven systems, the average noise should be defined operationally with care over which period of time is covered.