Full counting statistics of Luttinger liquid conductor

TL;DR

This paper derives an exact expression for the full counting statistics of charge transport in a Luttinger liquid conductor using non-equilibrium bosonization, revealing fractional charge effects due to interactions.

Contribution

It introduces a novel exact formula for charge counting statistics in interacting 1D systems, linking it to non-interacting particle models with fractional charges.

Findings

Exact full counting statistics expressed as a Fredholm determinant.

Charge fluctuations exhibit fractionalization due to interactions.

Results applicable to quantum wires with boundary scattering.

Abstract

Non-equilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the full counting statistics of the transmitted charge is derived. It is given by Fredholm determinant of the counting operator with a time dependent scattering phase. The result has a form of counting statistics of non-interacting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the non-interacting leads.