Time-dependent current density functional theory on a lattice

Details Time-dependent current density functional theory on a lattice Time-dependent current density functional theory on a lattice

2010-11-11

arxiv.org/abs/1011.2715v1

Phys. Rev. B 83, 035127 (2011)

Physics

Condensed Matter

Strongly Correlated Electrons

revtex4, 9 pages

Scientific paper

10.1103/PhysRevB.83.035127

A rigorous formulation of time-dependent current density functional theory (TDCDFT) on a lattice is presented. The density-to-potential mapping and the ${\cal V}$-representability problems are reduced to a solution of a certain nonlinear lattice Schr\"odinger equation, to which the standard existence and uniqueness results for nonliner differential equations are applicable. For two versions of the lattice TDCDFT we prove that any continuous in time current density is locally ${\cal V}$-representable (both interacting and noninteracting), provided in the initial state the local kinetic energy is nonzero everywhere. In most cases of physical interest the ${\cal V}$-representability should also hold globally in time. These results put the application of TDCDFT to any lattice model on a firm ground, and open a way for studying exact properties of exchange correlation potentials.

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