Overcoming obstacles in nonequilibrium holography

TL;DR

This paper investigates universal spatial features of non-equilibrium steady states in strongly correlated fluids, using holographic duality and hydrodynamics, revealing new behaviors with finite chemical potential and analyzing mode structures.

Contribution

It provides a field-theoretical definition of spatial collective modes and demonstrates their usefulness with new examples, including analytical solutions and the effects of finite chemical potential.

Findings

Identification of damped oscillatory behavior with chemical potential.

Transitions between oscillatory and damped regimes analyzed.

Demonstration of mode condensation into branch cuts at zero temperature.

Abstract

We study universal spatial features of certain non-equilibrium steady states corresponding to flows of strongly correlated fluids over obstacles. This allows us to predict universal spatial features of far-from-equilibrium systems, which in certain interesting cases depend cleanly on the hydrodynamic transport coefficients of the underlying theory, such as $\eta/s$, the shear viscosity to entropy density ratio. In this work we give a purely field-theoretical definition of the spatial collective modes identified earlier and proceed to demonstrate their usefulness in a set of examples, drawing on hydrodynamic theory as well as holographic duality. We extend our earlier treatment by adding a finite chemical potential, which introduces a qualitatively new feature, namely damped oscillatory behavior in space. We find interesting transitions between oscillatory and damped regimes and we consider critical exponents associated with these. We explain in detail the numerical method and add a host of new examples, including fully analytical ones. Such a treatment is possible in the large-dimension limit of the bulk theory, as well as in three dimensions, where we also exhibit a fully analytic non-linear example that beautifully illustrates the original proposal of spatial universality. This allows us to explicitly demonstrate how an infinite tower of discrete modes condenses into a branch cut in the zero-temperature limit, converting exponential decay into a power law tail.