### 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 language | English (US) |
---|---|

Article number | 075204 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 7 |

DOIs | |

State | Published - Feb 20 2015 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

}

**Beyond v-representability : Local one-body Hamiltonians for arbitrary densities.** / Lammert, Paul Edward.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Beyond v-representability

T2 - Local one-body Hamiltonians for arbitrary densities

AU - Lammert, Paul Edward

PY - 2015/2/20

Y1 - 2015/2/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84921796341&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921796341&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/48/7/075204

DO - 10.1088/1751-8113/48/7/075204

M3 - Article

AN - SCOPUS:84921796341

VL - 48

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 7

M1 - 075204

ER -