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Time-dependent V-representability on lattice systems

J. Chem. Phys. 129, 044105 (2008); doi:10.1063/1.2955733

Published 25 July 2008

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Yonghui Li and C. A. Ullrich
Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
We study the mapping between time-dependent densities and potentials for noninteracting electronic systems on lattices. As discovered recently by Baer [J. Chem. Phys. 128, 044103 (2008)], there exist well-behaved time-dependent density functions on lattices which cannot be associated with any real time-dependent potential. This breakdown of time-dependent V-representability can be tracked down to problems with the continuity equation which arise from discretization of the kinetic-energy operator. Examples are given for lattices with two points and with N points, and implications for practical numerical applications of time-dependent density-functional theory are discussed. In the continuum limit, time-dependent noninteracting V-representability is restored. ©2008 American Institute of Physics
History: Received 19 April 2008; accepted 13 June 2008; published 25 July 2008
Permalink: http://link.aip.org/link/?JCPSA6/129/044105/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.ee
    Time-dependent density functional theory (atoms and molecules)
  • YEAR: 2008

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ISSN:
0021-9606 (print)   1089-7690 (online)
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