Non-equilibrium steady states in quantum critical systems with Lifshitz scaling

TL;DR

This paper investigates out-of-equilibrium energy transport in quantum critical fluids with Lifshitz scaling, analyzing the formation and properties of steady states following local quenches across different dynamical critical exponents.

Contribution

It provides a comprehensive analysis of non-equilibrium steady states in Lifshitz fluids, including the solution of the Riemann problem and the characterization of steady states for arbitrary z.

Findings

Universal late-time energy flow in Lifshitz fluids

Steady states are boosted thermal states for z=2

Non-thermal steady states for generic z

Abstract

We study out-of-equilibrium energy transport in a quantum critical fluid with Lifshitz scaling symmetry following a local quench between two semi-infinite fluid reservoirs. The late time energy flow is universal and is accommodated via a steady state occupying an expanding central region between outgoing shock and rarefaction waves. We consider the admissibility and entropy conditions for the formation of such a non-equilibrium steady state for a general dynamical critical exponent z in arbitrary dimensions and solve the associated Riemann problem. The Lifshitz fluid with z=2 can be obtained from a Galilean boost invariant field theory and the non-equilibrium steady state is identified as a boosted thermal state. A Lifshitz fluid with generic z is scale invariant but without boost symmetry and in this case the non-equilibrium steady state is genuinely non-thermal.