Many-particle correlations in non-equilibrium Luttinger liquid

TL;DR

This paper introduces an exact operator-based method to analyze many-particle correlations in non-equilibrium Luttinger liquids, enabling precise calculation of fermionic correlation functions under interaction and non-equilibrium conditions.

Contribution

The authors develop a novel operator formalism that expresses non-equilibrium fermionic correlations as Fredholm determinants, allowing exact evaluation of all correlation functions in the model.

Findings

Exact expressions for fermionic correlation functions as Fredholm determinants.

Analysis of four-point correlation functions under non-equilibrium conditions.

Demonstration of the combined effects of interactions and non-equilibrium on fermionic distributions.

Abstract

We develop an operator-based approach to the problem of Luttinger liquid conductor in a non-equilibrium stationary state. We show that the coherent-state many-body fermionic density matrix as well as all fermionic correlation functions out of equilibrium are given by one-dimensional functional determinants of the Fredholm type. Thus, the model constitutes a remarkable example of a many-body problem where all the correlation functions can be evaluated exactly. On the basis of the general formalism we investigate four-point correlation functions of the fermions coming out of the Luttinger liquid wire. Obtained correlations in the fermionic distribution functions represent the combined effect of interaction and non-equilibrium conditions.