Time-dependent current density functional theory on a lattice

Physical Review B 83, 035127 (2011)

Time-dependent current density functional theory on a lattice

I. V. Tokatly

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

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Doi
http://dx.doi.org/10.1103/PhysRevB.83.035127
arxiv
http://arxiv.org/abs/arXiv:1011.2715

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