L2 Analysis of the Multi-Configuration Time-Dependent Hartree-Fock Equations
Mauser, Norbert; Trabelsi, Saber (2010), L2 Analysis of the Multi-Configuration Time-Dependent Hartree-Fock Equations, Mathematical Models and Methods in Applied Sciences, 20, 11. http://dx.doi.org/10.1142/S0218202510004842
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00453962
Journal nameMathematical Models and Methods in Applied Sciences
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Abstract (EN)The multi-configuration methods are widely used by quantum physicists/chemists for numerical approximation of the many electron Schrödinger equation. Recently, first mathematically rigorous results were obtained on the time-dependent models, e.g. short-in-time well-posedness in the Sobolev space H2 for bounded interactions20 with initial data in H2, in the energy space for Coulomb interactions with initial data in the same space,25,5 as well as global well-posedness under a sufficient condition on the energy of the initial data.4,5 The present contribution extends the analysis by setting an L2 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 the mass invariant.
Subjects / KeywordsMulti-configuration methods; Hartree-Fock equations; Strichartz estimates; regularity; existence
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