Full counting statistics for noninteracting fermions: Exact finite temperature results and generalized long time approximation

TL;DR

This paper derives exact finite-temperature full counting statistics for noninteracting fermions and generalizes the Levitov-Lesovik formula for quantum dot systems in the long time limit.

Contribution

It introduces a new approach to compute FCS at finite temperatures and extends the Levitov-Lesovik formula to more complex quantum dot systems.

Findings

Exact numerical FCS results at finite temperatures

New expression for cumulant generating function in quantum dot systems

Generalization of the Levitov-Lesovik formula

Abstract

Exact numerical results for the full counting statistics (FCS) of a one-dimensional tight-binding model of noninteracting electrons are presented at finite temperatures using an identity recently presented by Abanov and Ivanov. A similar idea is used to derive a new expression for the cumulant generating function for a system consisting of two quasi-one-dimensional leads connected by a quantum dot in the long time limit. This provides a generalization of the Levitov-Lesovik formula for such systems.