99 research outputs found
Analysis of the Multi-Configuration Time-Dependent Hartree-Fock Equations
The multiconfiguration methods are widely used by quantum physicists and
chemists for numerical approximation of the many electron Schr\"odinger
equation. Recently, first mathematically rigorous results were obtained on the
time-dependent models, e.g. short-in-time well-posedness in the Sobolev space
for bounded interactions (C. Lubichand O. Koch} with initial data in
, in the energy space for Coulomb interactions with initial data in the
same space (Trabelsi, Bardos et al.}, as well as global well-posedness under a
sufficient condition on the energy of the initial data (Bardos et al.). The
present contribution extends the analysis by setting an theory for the
MCTDHF for general interactions including the Coulomb case. This kind of
results is also the theoretical foundation of ad-hoc methods used in numerical
calculation when modification ("regularization") of the density matrix destroys
the conservation of energy property, but keeps invariant the mass.Comment: This work was supported by the Viennese Science Foundation (WWTF) via
the project "TDDFT" (MA-45), the Austrian Science Foundation (FWF) via the
Wissenschaftkolleg "Differential equations" (W17) and the START Project
(Y-137-TEC) and the EU funded Marie Curie Early Stage Training Site DEASE
(MEST-CT-2005-021122
Properties of nonfreeness: an entropy measure of electron correlation
"Nonfreeness" is the (negative of the) difference between the von Neumann
entropies of a given many-fermion state and the free state that has the same
1-particle statistics. It also equals the relative entropy of the two states in
question, i.e., it is the entropy of the given state relative to the
corresponding free state. The nonfreeness of a pure state is the same as its
"particle-hole symmetric correlation entropy", a variant of an established
measure of electron correlation. But nonfreeness is also defined for mixed
states, and this allows one to compare the nonfreeness of subsystems to the
nonfreeness of the whole. Nonfreeness of a part does not exceed that in the
whole; nonfreeness is additive over independent subsystems; and nonfreeness is
superadditive over subsystems that are independent on the 1-particle level.Comment: 20 pages. Submitted to Phys. Rev.
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