Non-dissipative electrically driven fluids

TL;DR

This paper introduces a new class of hydrodynamic states for charged fluids that incorporate an arbitrary zeroth order electric field, enabling consistent modeling of thermo-electric transport with non-zero DC currents.

Contribution

It develops a hydrodynamic framework with an arbitrary electric field at zeroth order, resolving previous theoretical constraints and generalizing the Drude model for charged fluids.

Findings

Derives explicit conductivity formulas depending non-linearly on electric field.

Identifies a new hydrostatic constraint on fluid velocity in charged fluids.

Demonstrates non-trivial thermo-electric transport at ideal order.

Abstract

Existing hydrodynamic models of charged fluids consider any external electric field acting on the fluid as either first order in the hydrodynamic derivative expansion and completely arbitrary or zeroth order but constrained by the fluid's chemical potential. This is in tension with experiments on charged fluids, where the electric field is both zeroth order and completely arbitrary. In this work, we take the first step at resolving this conundrum by introducing a new class of hydrodynamic stationary states, including an arbitrary zeroth order electric field, upon which hydrodynamics can be built. We achieve this by first writing down the hydrostatic constitutive relations for a boost-agnostic charged fluid up to first order in derivatives. Then we introduce suitable energy and momentum relaxation terms to balance the influence of the electric field on the fluid. This analysis leads to a new hydrostatic constraint on the spatial fluid velocity, which can be used to define our class of states. This constraint generalizes to the realm of hydrodynamics a similar constraint on the velocity found in the Drude model of electronic transport. Our class of states exhibits non-trivial thermo-electric transport even at ideal order, since it hosts non-zero DC electric and heat currents. We derive the explicit form of the corresponding conductivities and show they depend non-linearly on the electric field.