A hydrodynamic approach to non-equilibrium conformal field theories
Denis Bernard, Benjamin Doyon
TL;DR
The paper addresses non-equilibrium dynamics in one-dimensional conformal field theories perturbed by the irrelevant operator $T\bar{T}$, proposing a hydrodynamic framework that emerges at first order in the coupling $g$. It derives a closed, relativistic hydrodynamic description from local thermalization and conservation laws, obtaining a boosted equation of state and showing that the non-equilibrium steady state resides between two shock waves whose speeds coincide with the baths' sound velocities. The main results include explicit expressions for central-region quantities, a steady-state current $j_s$ that reflects left-right thermal differences, and conjectured scalings for approach to the steady state, $t^{-1/2}$, with shock widths growing as $t^{1/3}$; a complementary quantum-flow perspective via random Virasoro diffeomorphisms provides intuition for these scalings. The work offers a tractable, quantitative description of Neq-CFT transport under an irrelevant perturbation, with potential implications for universal non-equilibrium transport in gapless quantum systems and avenues to study fluctuations and higher-order effects.
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 $t^{1/3}$.