Speaker
R. Ekman
Description
See the full Abstract at http://ocs.ciemat.es/EPS2018ABS/pdf/P1.4018.pdf
Do hydrodynamical models underestimate exchange effects? Comparison
with kinetic theory for electrostatic waves
G. Brodin1 , R. Ekman1 , J. Zamanian1
1 Department of Physics, Umeå University, Umeå, Sweden
In dense or cold plasmas with degenerate electrons, the quantum mechanical effect of elec-
tron exchange can be important [1]. Quantum hydrodynamical models can include exchange
through a potential derived from time-independent functional theory (TIDFT) [2], but because
of the time-independence, the accuracy for dynamical problems is unclear. To investigate this
accuracy, we compare with a kinetic model that includes exchange effects [3, 4], for the case of
electrostatic waves [5].
Concretely, we compute the exchange correction to the electrostatic electron susceptibility for
all phase velocities, at T = 0 K. We find that for low phase velocities (ion acoustic waves), the
susceptibility in the kinetic model is an order of magnitude larger than the hydrodynamical one.
The large discrepancy is due to wave-particle interaction that is lost in fluid models. However,
for phase velocities large compared to the Fermi velocity (vϕ & 2.5vF ) the hydrodynamical and
kinetic susceptibilities agree rather well.
Our results have implications for model choice: for dense and cold plasmas, in addition to ex-
change, particle dispersive effects can be important. Relative to classical terms, the contributions
1/3
scale as H 2 = h̄2 ω p2 /m2e v4F ∝ ne in both cases, where ω p , me , ne are the electron plasma fre-
quency, mass, and number density, respectively. Because the numerical coefficient for exchange
can be large in the low-frequency regime, using a model which includes particle dispersion but
not exchange effects cannot be justified. As a further consequence, a quantum mechanical tre-
atment including exchange may be necessary for a modest value of H 2 ∼ 0.1, i.e., even for
electron densities somewhat below those of metals (for which H 2 ∼ 1).
References
[1] M. Bonitz, Quantum Kinetic Theory, (B.G. Teubner, Stuttgart, Leipzig, 1998).
[2] N. Crouseilles, P.-A Hervieux, and G. Manfredi, Phys. Rev. B, 78, 155412 (2008).
[3] J. Zamanian, M. Marklund, and G. Brodin, Phys. Rev. E 88, 063105 (2013).
[4] R. Ekman, J. Zamanian, and G. Brodin, Phys. Rev. E, 92, 013104 (2015).
[5] G. Brodin, R. Ekman, and J. Zamanian, in preparation.
