Statistics of charge transfer through impurities in strongly correlated 1D metals

TL;DR

This paper reviews recent analytic solutions for the full counting statistics of charge transfer through impurities in strongly correlated 1D metals modeled as Tomonaga-Luttinger liquids, focusing on non-trivial contacts.

Contribution

It provides a comprehensive review of exact analytic solutions for the cumulant generating function in charge transfer through impurities in TLLs.

Findings

Exact solutions for the cumulant generating function are available.

Application to non-trivial contacts between crossed TLLs.

Advances in understanding charge transfer statistics in strongly correlated 1D systems.

Abstract

We review recent advances in the field of full counting statistics (FCS) of charge transfer through impurities imbedded into strongly correlated one-dimensional metallic systems, modelled by Tomonaga-Luttinger liquids (TLLs). We concentrate on the exact analytic solutions for the cumulant generating function (CGF), which became available recently and apply these methods in order to obtain the FCS of a non-trivial contact between two crossed TLL.