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

作者：Lammert Paul E^*

来源：Journal of Physics A-Mathematical and Theoretical, 2015, 48(7): 075204.

DOI：10.1088/1751-8113/48/7/075204

• density functional theory
• nonstandard analysis
• v-representability

The 'v-representability problem' arising in density functional theory is this: for an 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 v? 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 nonstandard analysis) which is a simple function defined on a regular grid of infinitesimal finesse. At a vague conceptual level, therefore, the result is not far from universal v-representability.

• 出版日期2015-2-20