Translation-invariant quasi-free states for fermionic systems and the BCS approximation

DOI10.1142/S0129055X14500123zbMath1327.82099arXiv1305.5135MaRDI QIDQ2920917

Robert Seiringer, Christian Hainzl, Gerhard Bräunlich

Publication date: 29 September 2014

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.5135

zbMATH Keywords

superfluiditycritical temperatureBirman-Schwinger principlequasi-free statesBardeen-Cooper-Schrieffer functional

Mathematics Subject Classification ID

Statistical mechanics of superfluids (82D50) Applications of functional analysis in quantum physics (46N50)

Related Items (11)

The BCS energy gap at low density ⋮ Multi-component Ginzburg-Landau theory: microscopic derivation and examples ⋮ The Bogoliubov free energy functional. I: Existence of minimizers and phase diagram ⋮ Bogolubov-Hartree-Fock theory for strongly interacting fermions in the low density limit ⋮ A lower bound for the BCS functional with boundary conditions at infinity ⋮ Microscopic derivation of Ginzburg-Landau theory and the BCS critical temperature shift in general external fields ⋮ Microscopic derivation of Ginzburg-Landau theory and the BCS critical temperature shift in a weak homogeneous magnetic field ⋮ Vortex lattices and the Bogoliubov-de Gennes equations ⋮ Numerical solution of large scale Hartree–Fock–Bogoliubov equations ⋮ Persistence of translational symmetry in the BCS model with radial pair interaction ⋮ The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties

Cites Work

• On blowup for time-dependent generalized Hartree-Fock equations
• Minimizers for the Hartree-Fock-Bogoliubov theory of neutron stars and white dwarfs
• The BCS functional for general pair interactions
• The BCS critical temperature for potentials with negative scattering length
• Generalized Hartree-Fock theory and the Hubbard model
• The critical temperature for the BCS equation at weak coupling
• Microscopic derivation of Ginzburg-Landau theory
• Bogolubov–Hartree–Fock mean field theory for neutron stars and other systems with attractive interactions
• A NONLINEAR MODEL FOR RELATIVISTIC ELECTRONS AT POSITIVE TEMPERATURE
• A numerical perspective on Hartree−Fock−Bogoliubov theory
• Theory of Superconductivity

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