Jensen-Feynman approach to the statistics of interacting electrons

Journal Article · Sat Aug 15 00:00:00 EDT 2009 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.80.026703· OSTI ID:21344694

Pain, Jean-Christophe; Gilleron, Franck; Faussurier, Gerald ^[1]

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1. CEA, DAM, DIF, F-91297 Arpajon (France)

Faussurier et al. [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of canonical partition functions. It consists of a decomposition into a reference electron system and a first-order correction. The procedure appears to be very efficient in order to evaluate the free energy and the orbital populations. In this work, we present numerical applications of the method and propose to extend it using a reference energy which includes the interaction between two electrons inside a given orbital. This is possible, thanks to our efficient recursion relation for the calculation of partition functions. We also show that a linear reference energy, however, is usually sufficient to achieve a good precision and that the most promising way to improve the approach of Faussurier et al. is to apply Jensen's inequality to a more convenient convex function.

• OSTI ID: 21344694
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 80, Issue 2; Other Information: DOI: 10.1103/PhysRevE.80.026703; (c) 2009 The American Physical Society; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DECOMPOSITION
ELECTRON GAS
ELECTRON-ELECTRON COLLISIONS
ELECTRON-ELECTRON COUPLING
ELECTRON-ELECTRON INTERACTIONS
ELECTRONS
FREE ENERGY
PARTITION FUNCTIONS
QUANTUM MECHANICS
STATISTICS
VARIATIONAL METHODS
CALCULATION METHODS
CHEMICAL REACTIONS
COLLISIONS
COUPLING
ELECTRON COLLISIONS
ELEMENTARY PARTICLES
ENERGY
FERMIONS
FUNCTIONS
INTERACTIONS
LEPTON-LEPTON INTERACTIONS
LEPTONS
MATHEMATICS
MECHANICS
PARTICLE INTERACTIONS
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES