Existence of minimizers for the Dirac-Fock model of crystals

DOI10.1007/s00205-024-01988-8MaRDI QIDQ6583721

Eric Paturel, I. Catto, Long Meng, Éric Séré

Publication date: 6 August 2024

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Qxx) General mathematical topics and methods in quantum theory (81Qxx) Applications of quantum theory to specific physical systems (81Vxx)

Cites Work

• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Renormalization and asymptotic expansion of Dirac's polarized vacuum
• Ground state and charge renormalization in a nonlinear model of relativistic atoms
• Existence of atoms and molecules in the mean-field approximation of no-photon quantum electrodynamics
• Solutions of the Dirac-Fock equations and the energy of the electron-positron field
• A new approach to the modeling of local defects in crystals: The reduced Hartree-Fock case
• Properties of periodic Hartree-Fock minimizers
• Error bound for the Hartree-Fock energy of atoms and molecules
• Spectral theory of the operator \((p^2+m^2)^{1/2}-Ze^2/r\)
• The Thomas-Fermi theory of atoms, molecules and solids
• A minimax principle for eigenvalues in spectral gaps: Dirac operators with Coulomb potentials.
• On some periodic Hartree-type models for crystals
• Some connections between Dirac-Fock and electron-positron Hartree-Fock
• Perturbation theory for linear operators.
• Solutions of the Dirac-Fock equations for atoms and molecules
• Solutions of Hartree-Fock equations for Coulomb systems
• On the Hartree-Fock equations of the electron-positron field
• The relativistic self-consistent field.
• Remarks on the Mittleman max–min variational method for the electron-positron field
• Solutions of the Dirac-Fock equations without projector.
• On the thermodynamic limit for Hartree-Fock type models
• Nonrelativistic limit of the Dirac-Fock equations
• Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac-Coulomb operators
• A rigorous justification of the Mittleman's approach to the Dirac-Fock model
• A new definition of the Dirac-Fock ground state

This page was built for publication: Existence of minimizers for the Dirac-Fock model of crystals

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6583721)