Full counting statistics for noninteracting fermions: Joint probability distributions

TL;DR

This paper develops a simplified method to compute the joint probability distribution in full counting statistics for noninteracting electrons, providing explicit results for complex quantum systems like Y-junctions and multi-lead dots.

Contribution

It introduces a straightforward approach to derive the long-time behavior of the characteristic function and presents new explicit determinant formulas involving scattering matrices.

Findings

Derived explicit formulas for joint probability distributions in complex quantum systems.

Simplified the calculation of the long-time limit of the characteristic function.

Analyzed systems like Y-junctions and multi-lead quantum dots.

Abstract

The joint probability distribution in the full counting statistics (FCS) for noninteracting electrons is discussed for an arbitrary number of initially separate subsystems which are connected at t=0 and separated at a later time. A simple method to obtain the leading order long time contribution to the logarithm of the characteristic function is presented which simplifies earlier approaches. New explicit results for the determinant involving the scattering matrices are found. The joint probability distribution for two leads is discussed for Y-junctions and dots connected to four leads.