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Fermion N -representability for prescribed density and paramagnetic current density

Tellgren, Erik; Kvaal, Simen; Helgaker, Trygve
Journal article; PublishedVersion; Peer reviewed
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PhysRevA.89.012515.pdf (169.3Kb)
Year
2014
Permanent link
http://urn.nb.no/URN:NBN:no-59818

CRIStin
1106149

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  • Kjemisk institutt [925]
  • CRIStin høstingsarkiv [16845]
Original version
Physical Review A. Atomic, Molecular, and Optical Physics. 2014, 89 (1):012515, DOI: http://dx.doi.org/10.1103/PhysRevA.89.012515
Abstract
The N-representability problem is the problem of determining whether there exists N-particle states with some prescribed property. Here we report an affirmative solution to the fermion N-representability problem when both the density and the paramagnetic current density are prescribed. This problem arises in current-density functional theory and is a generalization of the well-studied corresponding problem (only the density prescribed) in density functional theory. Given any density and paramagnetic current density satisfying a minimal regularity condition (essentially that a von Weizäcker–like canonical kinetic energy density is locally integrable), we prove that there exists a corresponding N-particle state. We prove this by constructing an explicit one-particle reduced density matrix in the form of a position-space kernel, i.e., a function of two continuous-position variables. In order to make minimal assumptions, we also address mathematical subtleties regarding the diagonal of, and how to rigorously extract paramagnetic current densities from, one-particle reduced density matrices in kernel form.

© 2014 American Physical Society
 
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