Download Consequences for the Current-Density-Functional

Consequences for the Current-Density-Functional-Theory
from the exact solution of the two-electron-problem in a
magnetic field
Peter Machon
The manybody problem is a basic element of most physical applications in
the fields of solid state-, atomic and molecular-physics. A frequently used approach to solve this problem is density-functional-theory (DFT). To study the
properties of manybody systems in a magnetic field, extensions like spin-densityfunctional-theory (SDFT), current-density-functional-theory (CDFT) and spincurrent-density-functional-theory (SCDFT) are used. Topic of this talk is CDFT,
which was presented in 1988 by Vignale and Rasolt. The validity of central conditions of the CDFT coult not be shown yet.
The two-electron-problem in a harmonic confinement-potential with a magnetic field perpendicular to the plane is numerically exactly solvable. Based on
this solution it is shown that the extended Kohn-Sham-equations derived by
the semirelativistic CDFT do not yield the correct groudstate-properties as the
exact density and paramagnetic current-density derived from the exact solvable
system are not non-interacting-V-representable. The proof works free of assumptions as the necessary physical properties are based on the exact solution.
Additionally it is shown that this result holds true for the physical limits of
weakly and strongly correlated systems.
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