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 -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 points, and implications for practical numerical applications of time-dependent density-functional theory are discussed. In the continuum limit, time-dependent noninteracting -representability is restored.
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Research Article| July 25 2008
Time-dependent -representability on lattice systems
Yonghui Li, C. A. Ullrich; Time-dependent -representability on lattice systems. J. Chem. Phys. 28 July 2008; 129 (4): 044105. https://doi.org/10.1063/1.2955733
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