Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-dependent current density functional theory on a lattice   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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The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: comp-gas