The BCS functional of superconductivity and its mathematical properties

Abstract

We review recent results concerning the mathematical properties of the Bardeen-Cooper-Schrieffer (BCS) functional of superconductivity, which were obtained in a series of papers partly in collaboration with R. Frank, E. Hamza, S. Naboko, and J.P. Solovej. Our discussion includes, in particular, an investigation of the critical temperature for a general class of interaction potentials, as well as a study of its dependence on external fields. We shall explain how the Ginzburg-Landau model can be derived from the BCS theory in a suitable parameter regime.

54 pages

References in corpus (6)

• Many-Body Physics with Ultracold Gases
• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• A Nonlinear Model for Relativistic Electrons at Positive Temperature
• The BCS Critical Temperature for Potentials with Negative Scattering Length
• The external field dependence of the BCS critical temperature

Cited by in corpus (28)

• Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
• Bosonic quadratic Hamiltonians
• Reduced Density Matrix Functional Theory for Superconductors
• Lower Bound on the Hartree-Fock Energy of the Electron Gas
• Ubiquity of superconducting domes in BCS theory with finite-range potentials
• Bogolubov-Hartree-Fock theory for strongly interacting fermions in the low density limit
• Persistence of translational symmetry in the BCS model with radial pair interaction
• The BCS Energy Gap at High Density
• General pairing mechanisms in the BCS-theory of superconductivity
• The BCS Critical Temperature at High Density
• Bounds on $T_c$ in the Eliashberg theory of Superconductivity. I: The $\gamma$-model
• Universality in low-dimensional BCS theory
• Universal and nonuniversal features of Bardeen-Cooper-Schrieffer theory with finite-range interactions
• BCS Critical Temperature on Half-Spaces
• The BCS Energy Gap at Low Density
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field
• A lower bound for the BCS functional with boundary conditions at infinity
• Mixed parity pairing in a dipolar gas
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields
• An operator-theoretical study of the specific heat and the critical magnetic field in the BCS-Bogoliubov model of superconductivity
• Another operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity
• Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical Temperature
• An operator-theoretical study on the BCS-Bogoliubov model of superconductivity near absolute zero temperature
• Dynamics of mean-field Fermi systems with nonzero pairing
• Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition
• Enhanced Superconductivity at a Corner for the Linear BCS Equation
• Enhanced pairing mechanism in Cuprate-type crystals
• Differential Equations of Quantum Mechanics