Heidelberg 1999 – scientific programme
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A: Atomphysik
A 14: Poster
A 14.35: Poster
Thursday, March 18, 1999, 16:30–19:00, PY
The collisionless hydrodynamical theory for an electron gas. — •I. Tokatly and O. Pankratov — Lehrstuhl für theoretische Festkörperohysik, Universit"at Erlangen-N"urnberg, Staudtstr.7, 91058 Erlangen
A long time ago Tomas and Fermi have shown a possibility of a simple
statistical description of equilibrium electronic liquids if quasiclassical
conditions are satisfied. Shortly afterwards Bloch proposed a dynamical
extention of the TF theory, which, with some modifications, is commonly used
till now. However Bloch’s hydrodynamical theory (HT) shows an inconsistency
that has been reflected in many textbooks. The velocity coefficient in the
plasmon dispersion law ω=ωp + v2k2 equals the sound velocity
vs2 in HT instead of the correct value <vp2>, which follows from
collisionless kinetic theory.
We found that the origin of this discrepancy is the common assumption for quasi
equilibrium distribution function, which reduces the kinetic equation to HT
with one scalar (density) and one vector (velocity) field. These fields
describe changes of radius of the Fermi sphere and its shift in the momentum
space during evolution of initial distribution function. We show that a
correct derivation of HT as a long-wave limit of kinetic theory inevitably
leads to the appearance of a tensor field of momentum flux, which has a
traceless part responsible for distortion of the shape of Fermi surface. The
traceless part of the momentum flux tensor is of the same order in a gradient
expansion as the common terms in Euler equation. The resulting HT does not
require any assumptions concerning the dynamical equation of state, which is
totally follows from HT. In contrast to Bloch’s theory, the new HT leads to
the correct velocity in the plasmon dispersion.