Shock waves, rarefaction waves and non-equilibrium steady states in quantum critical systems

TL;DR

This paper investigates the formation of non-equilibrium steady states in quantum critical systems after a local quench, revealing that energy transport occurs via shock and rarefaction waves, with universal properties independent of microscopic details.

Contribution

It demonstrates that energy transport in quantum critical systems involves shock and rarefaction waves, correcting previous models that suggested two shock waves, and shows the universality of the steady state.

Findings

Energy transport involves shock and rarefaction waves.

Universal steady state energy currents are independent of microscopic details.

Differences between solutions are within two percent across parameters.

Abstract

We re-examine the emergence of a universal non-equilibrium steady state following a local quench between quantum critical heat baths in spatial dimensions greater than one. We show that energy transport proceeds by the formation of an instantaneous shock wave and a broadening rarefaction wave on either side of the interface, and not by two shock waves as previously proposed. For small temperature differences the universal steady state energy currents of the two-shock and rarefaction-shock solutions coincide. Over a broad range of parameters, the difference in the energy flow across the interface between these two solutions is at the level of two percent. The properties of the energy flow remain fully universal and independent of the microscopic theory. We briefly discuss the width of the shock wave in a viscous fluid, the effects of momentum relaxation, and the generalization to charged fluids.