Dissipative electrically driven fluids

https://arxiv.org/abs/2407.18856

The sequel to "Non-dissipative electrically driven fluids". As a reminder, in the previous paper my colleagues and I developed a formalism to describe the stationary behaviour of a fluid inside an external electric field. This was only possible in the presence of energy and momentum relaxation terms which act to remove these same quantities from the fluid (the electric field adds energy and momentum).  This formalism was developed to help explain the behaviour of strange metals whose effective description is expected to be hydrodynamic.

Strange metals are enigmatic states of matter found in high temperature superconductors. Their resistivity does not scale with temperature in the way one would expect from the leading perturbative description of metals - Landau-Fermi liquid theory. This led researchers to posit the idea that the microscopic nature of the material is in fact strongly coupled. If this was true it would mean  that any effective description should be hydrodynamics as all other perturbations would rapidly decay away. This birthed a whole field of holographic models trying to better capture the features of these materials (for example, including charge density waves). However, one common feature to all these models was the contribution of a particular transport coefficient - which for want of  a better name I will call the incoherent conductivity - to the DC conductivity of the system. By tuning this coefficient it was possible to reproduce the correct temperature scaling of the resistivity.

In "Dissipative electrically driven fluids" we extended our ealier formalism to include dissipative corrections in the presence of an order one in derivative external electric field. This allows us to ask  questions about the conductivity of fluids which achieve a stationary state in a driving electric field. We showed how positivity of entropy production and Onsager reciprocity further constrain transport in the fluid. 

Most importantly, we confirmed our guess from "Non-dissipative electrically driven fluids" and showed that for Onsager reciprocal fluids it is not possible  for the incoherent conductivity to make a contribution to the DC. The earlier error stemmed from using holographic models whose stationarity conditions do not allow the holographic fluid to reach a steady driven state. This has important implications for the strange metal holographic programme - in particular, we now know that older models cannot correctly capture the physics.