Full counting statistics for voltage and dephasing probes

TL;DR

This paper introduces a stochastic path integral method to compute the full counting statistics of conductors with dephasing and voltage probes, validated on a Mach-Zehnder interferometer and generalizable to complex setups.

Contribution

A novel stochastic path integral approach for calculating full counting statistics in systems with dephasing and voltage probes, applicable to various geometries.

Findings

Method matches phase averaging results for dephasing

Applicable to Mach-Zehnder interferometers and beyond

Generalizes to complex conductor geometries

Abstract

We present a stochastic path integral method to calculate the full counting statistics of conductors with energy conserving dephasing probes and dissipative voltage probes. The approach is explained for the experimentally important case of a Mach-Zehnder interferometer, but is easily generalized to more complicated setups. For all geometries where dephasing may be modeled by a single one-channel dephasing probe we prove that our method yields the same full counting statistics as phase averaging of the cumulant generating function.