Beyond v-representability: Local one-body Hamiltonians for arbitrary densities

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The 'ν-representability problem' arising in density functional theory is this: for an script N-particle system of interacting identical particles, can every one-particle density of finite intrinsic energy be realized as a ground-state density upon modifying the Hamiltonian by addition of an appropriate external one-body potential ν? The answer is known to be no. We show that the answer is yes, if the inter-particle interaction is bounded, and allowed modifications are broadened from one-body potentials to local one-body operators. The required operator is obtained from a non-standard potential (in the sense of non-standard analysis) which is a simple function defined on a regular grid of in finitesimal finesse. At a vague conceptual level, therefore, the result is not far from universal ν-representability.

Original languageEnglish (US)
Article number075204
JournalJournal of Physics A: Mathematical and Theoretical
Issue number7
StatePublished - Feb 20 2015

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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