Time-dependent V-representability on lattice systems

Details Time-dependent V-representability on lattice systems Time-dependent V-representability on lattice systems

2008-04-18

arxiv.org/abs/0804.3114v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

8 pages, 4 figures

Scientific paper

10.1063/1.2955733

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.

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