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Title: Generalization of Lieb's variational principle to Bogoliubov–Hartree–Fock theory

In its original formulation, Lieb's variational principle holds for fermion systems with purely repulsive pair interactions. As a generalization we prove for both fermion and boson systems with semi-bounded Hamiltonian that the infimum of the energy over quasifree states coincides with the infimum over pure quasifree states. In particular, the Hamiltonian is not assumed to preserve the number of particles. To shed light on the relation between our result and the usual formulation of Lieb's variational principle in terms of one-particle density matrices, we also include a characterization of pure quasifree states by means of their generalized one-particle density matrices.
Authors:
; ;  [1] ;  [2]
  1. Technische Universität Braunschweig, Institut für Analysis und Algebra, Rebenring 31, 38106 Braunschweig (Germany)
  2. FernUniversität in Hagen, Fakultät für Mathematik und Informatik, Lehrgebiet Angewandte Stochastik, 58084 Hagen (Germany)
Publication Date:
OSTI Identifier:
22250854
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOSONS; DENSITY MATRIX; FERMIONS; HAMILTONIANS; PAIRING INTERACTIONS; VARIATIONAL METHODS