Existence, uniqueness, and construction of the density-potential mapping in time-dependent density-functional theory
Ruggenthaler, M., Penz, M., & van Leeuwen, R. (2015). Existence, uniqueness, and construction of the density-potential mapping in time-dependent density-functional theory. Journal of Physics: Condensed Matter, 27(20), Article 203202. https://doi.org/10.1088/0953-8984/27/20/203202
Julkaistu sarjassa
Journal of Physics: Condensed MatterPäivämäärä
2015Tekijänoikeudet
© 2015 IOP Publishing Ltd. Content from this work may be used under the terms of
the Creative Commons Attribution 3.0 licence.
In this work we review the mapping from densities to potentials in quantum mechanics, which is
the basic building block of time-dependent density-functional theory and the Kohn–Sham
construction. We first present detailed conditions such that a mapping from potentials to densities
is defined by solving the time-dependent Schrodinger equation. We specifically discuss intricacies ¨
connected with the unboundedness of the Hamiltonian and derive the local-force equation. This
equation is then used to set up an iterative sequence that determines a potential that generates a
specified density via time propagation of an initial state. This fixed-point procedure needs the
invertibility of a certain Sturm–Liouville problem, which we discuss for different situations. Based
on these considerations we then present a discussion of the famous Runge–Gross theorem which
provides a density-potential mapping for time-analytic potentials. Further we give conditions such
that the general fixed-point approach is well-defined and converges under certain assumptions.
Then the application of such a fixed-point procedure to lattice Hamiltonians is discussed and the
numerical realization of the density-potential mapping is shown. We conclude by presenting an
extension of the density-potential mapping to include vector-potentials and photons.
...
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0953-8984Asiasanat
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