PIRSA:13010105 Scientific Series Quantum Information

DOI10.48660/13010105

Series: Perimeter Institute Quantum Discussions

Schilling, C. (2013). Pinning of Fermionic Occupation Numbers. Perimeter Institute. https://pirsa.org/13010105

Schilling, Christian. Pinning of Fermionic Occupation Numbers. Perimeter Institute, Jan. 21, 2013, https://pirsa.org/13010105 

@misc{ pirsa_PIRSA:13010105,
  doi = {10.48660/13010105},
  url = {https://pirsa.org/13010105},
  author = {Schilling, Christian},
  keywords = {Quantum Information},
  language = {en},
  title = {Pinning of Fermionic Occupation Numbers},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {jan},
  note = {PIRSA:13010105 see, \url{https://pirsa.org}}
}

Abstract

The problem of determining and describing the family of 1-particle reduced density operators (1-RDO) arising from N-fermion pure states (viapartial trace) is known as the fermionic quantum marginal problem. We present its solution, a multitude of constraints on the eigenvalues of the 1-RDO, generalizing the Pauli exclusion principle. To explore the relevance of these constraints we study an analytically solvable model of N fermions in a harmonic potential and determine the spectral `trajectory' corresponding to the ground state as function of the fermion-fermion interaction strength.Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasi-pinned). Our findings suggest a generalization of the Hartree-Fock approximation.

see also: http://arxiv.org/abs/1210.5531

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