The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties

DOI10.1063/1.4941723zbMath1360.81315arXiv1511.01995OpenAlexW3099387729MaRDI QIDQ2795510

Robert Seiringer, Christian Hainzl

Publication date: 21 March 2016

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

Full work available at URL: https://arxiv.org/abs/1511.01995

zbMATH Keywords

superconductivityGinzburg-Landau modelBardeen-Cooper-Schrieffer functional

Mathematics Subject Classification ID

Statistical mechanics of superconductors (82D55) Composite media; random media in optics and electromagnetic theory (78A48) Ginzburg-Landau equations (35Q56) Other fundamental interactions in quantum theory (81V19)

Related Items (19)

The BCS energy gap at low density ⋮ The BCS energy gap at high density ⋮ Numerical calculation of the left and right fractional derivatives ⋮ 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 ⋮ Equilibrium and non-equilibrium properties of superfluids and superconductors ⋮ Bosonic quadratic Hamiltonians ⋮ Microscopic derivation of Ginzburg-Landau theory and the BCS critical temperature shift in general external fields ⋮ Quantitative bounds versus existence of weakly coupled bound states for Schrödinger type operators ⋮ 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 ⋮ Persistence of translational symmetry in the BCS model with radial pair interaction ⋮ Condensation of fermion pairs in a domain ⋮ Quasi-particles, thermodynamic consistency, and the gap equation ⋮ Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms ⋮ Spin Symmetry Breaking in the Translation-Invariant Hartree--Fock Electron Gas ⋮ The BCS critical temperature at high density ⋮ The BCS critical temperature in a weak homogeneous magnetic field ⋮ Differential equations of quantum mechanics

Cites Work

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• Multi-component Ginzburg-Landau theory: microscopic derivation and examples
• Low density limit of BCS theory and Bose-Einstein condensation of fermion pairs
• On the Bardeen-Cooper-Schrieffer integral equation in the theory of superconductivity
• Spectral methods in surface superconductivity
• The BCS functional for general pair interactions
• The BCS critical temperature for potentials with negative scattering length
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• Generalized Hartree-Fock theory and the Hubbard model
• The critical temperature for the BCS equation at weak coupling
• On the mathematical structure of the B.C.S.-model
• An existence proof for the gap equation in the superconductivity theory
• Dynamics of Bose-Einstein condensates of fermion pairs in the low density limit of BCS theory
• The uniqueness and approximation of a positive solution of the Bardeen–Cooper–Schrieffer gap equation
• On the BCS gap equation for superfluid fermionic gases
• Derivation of Ginzburg-Landau Theory for a One-dimensional System with Contact Interaction
• Microscopic derivation of Ginzburg-Landau theory
• Translation-invariant quasi-free states for fermionic systems and the BCS approximation
• Asymptotic behavior of eigenvalues of Schrödinger type operators with degenerate kinetic energy
• Statics and dynamics of magnetic vortices and of Nielsen–Olesen (Nambu) strings
• Spectral properties of the BCS gap equation of superfluidity
• A NONLINEAR MODEL FOR RELATIVISTIC ELECTRONS AT POSITIVE TEMPERATURE
• Vortex Analysis in the Ginzburg-Landau Model of Superconductivity
• The mathematical structure of the bardeen-cooper-schrieffer model
• Theory of Superconductivity
• The external field dependence of the BCS critical temperature

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