Collisionless hydrodynamics for one-dimensional motion of inhomogeneous degenerate electron gases: equivalence of two recent descriptions

Abstract

Recently Tokatly and Pankratov (TP) [Phys. Rev. B 60, 15 550 (1999)] used velocity moments of a classical kinetic equation to derive a hydrodynamic description of the motion of an electron gas. Independently, the present authors [Theochem 501-502, 327 (2000)] used considerations arising from the Harmonic Potential Theorem [Phys. Rev. Lett. 73, 2244 (1994)] to generate a form of high-frequency hydrodynamics for inhomogeneous degenerate electron gases (HPT-N3 hydrodynamics). We show here that TP hydrodynamics yields HPT-N3 hydrodynamics when linearized about a Thomas-Fermi ground state with one-dimensional spatial inhomogeneity.