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

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.