Reduced Dynamics of Full Counting Statistics

TL;DR

This paper develops a theory for modified reduced dynamics incorporating counting fields, enabling efficient computation of long-time full counting statistics in open quantum systems, demonstrated on the Anderson impurity model.

Contribution

It introduces a novel approach to derive reduced dynamics with counting fields, facilitating long-time statistical analysis from short-time simulations.

Findings

Efficiently computes long-time current in the Anderson impurity model.

Shows reduced dynamics with counting fields can handle system-environment observables.

Demonstrates applicability to nonequilibrium quantum transport problems.

Abstract

We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mixed system--environment observables, as well as their statistical properties, can be evaluated by considering counting fields. Given a numerical method able to simulate the field-modified dynamics over the memory timescale, we show that the long-lived full counting statistics can be efficiently obtained from the reduced dynamics. We demonstrate the utility of the technique by computing the long-time current in the nonequilibrium Anderson impurity model from short-time Monte Carlo simulations.