Non-equilibrium steady-states in conformal field theory

TL;DR

This paper constructs and analyzes universal non-equilibrium steady states in one-dimensional quantum critical systems using conformal field theory, revealing fluctuation properties and their relation to linear response functions.

Contribution

It introduces a scattering-based construction of steady states in conformal field theories and computes universal large deviation functions for energy and charge transfers.

Findings

Steady states converge at large times in quantum critical systems.

Large deviation functions depend only on fundamental constants and system parameters.

Fluctuation relations are satisfied by the computed large deviation functions.

Abstract

We present a construction of non-equilibrium steady states in one-dimensional quantum critical systems carrying energy and charge fluxes. This construction is based on a scattering approach within a real-time hamiltonian reservoir formulation. Using conformal field theory techniques, we prove convergence towards steady states at large time. We discuss in which circumstances these states describe the universal non-equilibrium regime at low temperatures. We compute the exact large deviation functions for both energy and charge transfers, which encode for the quantum and statistical fluctuations of these transfers at large time. They are universal, depending only on fundamental constants (h, k_B), on the central charge and on the external parameters such as the temperatures or the chemical potentials, and they satisfy fluctuation relations. A key point consists in relating the derivatives of these functions to the linear response functions but at complex shifted external parameters.