Energy flow in non-equilibrium conformal field theory

TL;DR

This paper analyzes energy flow and fluctuations in non-equilibrium 1D conformal field theories, revealing universal steady states and fluctuation relations, with a novel classical Poisson process representation of quantum fluctuations.

Contribution

It provides a general description of non-equilibrium steady states in conformal field theory and introduces a simple classical Poisson process model for quantum energy fluctuations.

Findings

Steady states are reached in non-equilibrium conformal systems.

Universal fluctuation relations are satisfied.

Quantum fluctuations are represented by classical Poisson processes.

Abstract

We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.