Overcoming obstacles in nonequilibrium holography

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 η/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.

Hydrodynamics without boosts

“…thec) plus equation of state data. 4 So far, we have ensured that second derivative terms vanish, and computed the resulting quadratic form explicitly (2.33). We note that there are 22 coefficients appearing in the quadratic form but there are a total of 29 transport coefficients, and so we expect there to be non-dissipative combinations of transport coefficients which we will enumerate in the next section 2.3.1.…”

“…obtained from this dispersion relation by fixing ω = 0 (or more generally, ω ∈ R) and continuing to complex momenta k ∈ C d , yielding a dispersion relation of the form k i (v j ) describing how decay lengths in stationary systems depend on background velocity [3,4].…”

“…The main impetus to develop the general theory, apart from being structurally interesting, is of course that situations arise in which the least symmetric theory is the only one applicable. For example, in order to clarify the distinction between ordinary quasi-normal modes and the spatial collective modes of [3,4] one should look to non-boost invariant systems. A non-relativistic hydrodynamic theory without Galilean invariance is furthermore needed to describe the electron fluid of graphene at finite carrier density [5,6].…”

“…These coefficients are provided in a companion notebook to the paper 4. These coefficients are provided in a companion notebook to the paper.…”

Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential

“…In a different context, collision between hydrodynamic sound mode and the hydrodynamic diffusion mode was already observed in[39].…”