Hydrodynamic theory of an electron gas

TL;DR

This paper develops a generalized hydrodynamic theory for an electron gas that accurately predicts plasmon dispersion and connects to viscous fluid theory, extending beyond local equilibrium assumptions.

Contribution

It introduces a non-local equilibrium hydrodynamic framework including higher moments, improving upon Bloch hydrodynamics and aligning with Navies-Stocks hydrodynamics in low-frequency limits.

Findings

Correct plasmon dispersion prediction

Recovers Navies-Stocks hydrodynamics at low frequencies

Links to viscous fluid theory in linear approximation

Abstract

The generalised hydrodynamic theory of an electron gas, which does not rely on an assumption of a local equilibrium, is derived as the long-wave limit of a kinetic equation. Apart from the common hydrodynamics variables the theory includes the tensor fields of the higher moments of the distribution function. In contrast to the Bloch hydrodynamics, the theory leads to the correct plasmon dispersion and in the low frequency limit recovers the Navies-Stocks hydrodynamics. The linear approximation to the generalised hydrodynamics is closely related to the theory of highly viscous fluids.