Time-dependent density functional theory on a lattice

Time-dependent density functional theory (TDDFT) for quantum many-body systems on a lattice is formulated rigorously. We prove the uniqueness of the density-to-potential mapping and demonstrate that a given density is [upsilon] representable if the initial many-body state and the density satisfy cer...

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Veröffentlicht in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2012-09, Vol.86 (12), Article 125130
Hauptverfasser: Farzanehpour, M., Tokatly, I. V.
Format: Artikel
Sprache:eng
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Zusammenfassung:Time-dependent density functional theory (TDDFT) for quantum many-body systems on a lattice is formulated rigorously. We prove the uniqueness of the density-to-potential mapping and demonstrate that a given density is [upsilon] representable if the initial many-body state and the density satisfy certain well-defined conditions. In particular, we show that for a system evolving from its ground state any density with a continuous second time derivative is locally in time [upsilon] representable and therefore the lattice TDDFT is guaranteed to exist. The TDDFT existence and uniqueness theorem is valid for any connected lattice, independently of its size, geometry, and/or spatial dimensionality. General statements of the existence theorem are illustrated on a pedagogical exactly solvable example, which displays all the details and subtleties of the proof in a transparent form. In conclusion we briefly discuss remaining open problems and directions for future research.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.86.125130