title: Time-dependent V-representability on lattice systems.
abstract: 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.
authors.affiliation: Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA.
authors.forename: Yonghui
authors.initials: Y
authors.lastname: Li
authors.forename: C A
authors.initials: CA
authors.lastname: Ullrich