A one-channel conductor in an ohmic environment: mapping to a TLL and full counting statistics

TL;DR

This paper maps a one-channel conductor in an ohmic environment to a TLL, enabling non-perturbative analysis of environmental effects on current-voltage characteristics and establishing an exact link between Coulomb blockade and shot noise.

Contribution

It introduces a mapping that allows exact analysis of environmental effects on mesoscopic conductors and relates Coulomb blockade to shot noise.

Findings

Derived non-perturbative I-V curves considering environment effects

Established an exact relationship between Coulomb blockade and shot noise

Determined full counting statistics at zero temperature

Abstract

It is shown that a one-channel mesoscopic conductor in an ohmic environment can be mapped to the problem of a backscattering impurity in a Tomonaga-Luttinger liquid (TLL). This allows to determine non perturbatively the effect of the environment on $I-V$ curves, and to find an exact relationship between dynamic Coulomb blockade and shot noise. We investigate critically how this relationship compares to recent proposals in the literature. The full counting statistics is determined at zero temperature.