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

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Abstract

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
Volume48
Issue number7
DOIs
StatePublished - Feb 20 2015

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Hamiltonians
Representability
Particle interactions
Ground state
Density functional theory
Arbitrary
Nonstandard Analysis
operators
Particle System
particle interactions
Operator
Density Functional
Ground State
grids
density functional theory
Grid
ground state
Energy
Interaction
energy

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

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abstract = "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.",
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