Full-counting statistics of time-dependent conductors

TL;DR

This paper introduces an efficient method for calculating the full-counting statistics of time-dependent quantum conductors using a hierarchy of generalized density operators, improving numerical stability and applicability to complex time-dependent scenarios.

Contribution

It presents a novel hierarchy-based approach for computing full-counting statistics in time-dependent Markovian systems, outperforming traditional number-resolved master equations.

Findings

Validated method on time-independent problems

Analyzed cumulants in adiabatic passage scenarios

Studied interference effects in double quantum dots

Abstract

We develop a scheme for the computation of the full-counting statistics of transport described by Markovian master equations with an arbitrary time dependence. It is based on a hierarchy of generalized density operators, where the trace of each operator yields one cumulant. This direct relation offers a better numerical efficiency than the equivalent number-resolved master equation. The proposed method is particularly useful for conductors with an elaborate time-dependence stemming, e.g., from pulses or combinations of slow and fast parameter switching. As a test bench for the evaluation of the numerical stability, we consider time-independent problems for which the full-counting statistics can be computed by other means. As applications, we study cumulants of higher order for two time-dependent transport problems of recent interest, namely steady-state coherent transfer by adiabatic passage and Landau-Zener-St\"uckelberg-Majorana interference in an open double quantum dot.