A hydrodynamic approach to non-equilibrium conformal field theories

TL;DR

This paper develops a hydrodynamic framework for non-equilibrium conformal field theories, specifically analyzing steady states in perturbed 1D CFTs and predicting shock behavior and approach dynamics.

Contribution

It introduces a hydrodynamic description for non-equilibrium 1D CFTs with $Tar T$ perturbation, linking quantum computations to fluid dynamics and shock phenomena.

Findings

Hydrodynamic description accurately models steady states and shock waves.

Shock velocities are modified by perturbation, matching sound velocities.

The approach to steady state follows a power law decay of t^{-1/2}.

Abstract

We develop a hydrodynamic approach to non-equilibrium conformal field theory. We study non-equilibrium steady states in the context of one-dimensional conformal field theory perturbed by the $T\bar T$ irrelevant operator. By direct quantum computation, we show, to first order in the coupling, that a relativistic hydrodynamic emerges, which is a simple modification of one-dimensional conformal fluids. We show that it describes the steady state and its approach, and we provide the main characteristics of the steady state, which lies between two shock waves. The velocities of these shocks are modified by the perturbation and equal the sound velocities of the asymptotic baths. Pushing further this approach, we are led to conjecture that the approach to the steady state is generically controlled by the power law $t^{-1/2}$, and that the widths of the shocks increase with time according to $t^{1/3}$.