Non-dissipative electrically driven fluids

https://arxiv.org/abs/2211.05791

The effect of external electric fields on charged fluids has received scant attention in the fluid/gravity literature. One of the rare exceptions is a work by Kovtun, which deals with spatially varying stationary configurations of a fluid in such a field. However, the situation presented in that paper is somewhat unique as the external electric field is balanced against a precisely modulated chemical potential. This is not what typically happens in nature.

In an electric field, charged particles will begin to accelerate. Without the presence of some opposing force to reduce their acceleration, particles will gain more and more energy. This appears in the correlators of hydrodynamics as an infinite DC conductivity.  There have been multiple work-arounds used in the literature, from ad-hoc relaxation terms that appear at the linearised level but otherwise vanish at thermodynamic equilibrium, to the introduction of translation breaking scalars that ameliorate some of the problems.

In this work we set out to incorporate relaxation terms into the definition of equilibrium. A guiding model for us was the Drude model of electron transport in a metal, although this is in practice  far from how charge flows in such materials. We  describe how one can modify stationarity conditions to account for the fact that there is an opposing force to an applied electric field. Finally, we argue that the DC conductivity for the stationary driven states we describe has precisely the Drude form.