Stochastic Path Integral Formulation of Full Counting Statistics

TL;DR

This paper develops a stochastic path integral approach to analyze full counting statistics in semi-classical systems, enabling calculation of charge distribution propagators and current cumulants.

Contribution

It introduces a novel path integral formalism for counting statistics and generalizes it to systems with multiple counting fields and charges.

Findings

Derived the propagator for charge distributions with multiple counting fields.

Calculated current cumulants in a hot-electron chaotic cavity.

Provided a saddle point approximation method for semi-classical counting statistics.

Abstract

We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the saddle point approximation to the path integral, and fluctuations around the saddle point are suppressed in the semi-classical approximation. We use this approach to derive the current cumulants of a chaotic cavity in the hot-electron regime.