Luttinger Liquid in Non-equilibrium Steady State

TL;DR

This paper presents an exactly solvable model of non-equilibrium Luttinger liquids on a star graph, analyzing transport, correlations, and steady states driven by heat baths with different temperatures and chemical potentials.

Contribution

It introduces a novel exactly solvable model for non-equilibrium Luttinger liquids on a multi-terminal junction with explicit steady state construction and non-equilibrium bosonization.

Findings

Explicit steady state constructed for non-equilibrium Luttinger liquid.

Derived exact current-current correlation functions and noise power.

Analyzed charge and heat transport in the non-equilibrium setting.

Abstract

We propose and investigate an exactly solvable model of non-equilibrium Luttinger liquid on a star graph, modeling a multi-terminal quantum wire junction. The boundary condition at the junction is fixed by an orthogonal matrix S, which describes the splitting of the electric current among the leads. The system is driven away from equilibrium by connecting the leads to heat baths at different temperatures and chemical potentials. The associated non-equilibrium steady state depends on S and is explicitly constructed. In this context we develop a non-equilibrium bosonization procedure and compute some basic correlation functions. Luttinger liquids with general anyon statistics are considered. The relative momentum distribution away from equilibrium turns out to be the convolution of equilibrium anyon distributions at different temperatures. Both the charge and heat transport are studied. The exact current-current correlation function is derived and the zero-frequency noise power is determined.