A hydrodynamic approach to non-equilibrium conformal field theories

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 $t^{1/3}$.

24 pages

References in corpus (7)

• Quantum Quench in the Transverse Field Ising Chain
• Quantum limit of heat flow across a single electronic channel
• Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
• Stationary states in a free fermionic chain from the Quench Action Method
• Energy transport in Heisenberg chains beyond the Luttinger liquid paradigm
• Luttinger Liquid in Non-equilibrium Steady State
• Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas

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