Spectral properties of the BCS gap equation of superfluidity

Abstract

We present a review of recent work on the mathematical aspects of the BCS gap equation, covering our results of [arXiv:0801.4159] as well our recent joint work with Hamza and Solovej [arXiv:math-ph/0703086] and with Frank and Naboko [arXiv:0704.3564], respectively. In addition, we mention some related new results.

Plenary talk given by C. Hainzl at QMath10, Moeciu, Romania, September 10-15, 2007

References in corpus (2)

• Many-Body Physics with Ultracold Gases
• Critical Temperature and Energy Gap for the BCS Equation

Cited by in corpus (11)

• The BCS functional of superconductivity and its mathematical properties
• Translation-invariant quasi-free states for fermionic systems and the BCS approximation
• The BCS gap equation for spin-polarized fermions
• Persistence of translational symmetry in the BCS model with radial pair interaction
• A mathematical proof that the transition to a superconducting state is a second-order phase transition
• 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
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields
• Smoothness of the Gap Function in the BCS-Bogoliubov Theory of Superconductivity
• On the number and sums of eigenvalues of Schrödinger-type operators with degenerate kinetic energy
• The BCS Gap Equation on a Banach Space Consisting of Functions both of the Temperature and of the Wave Vector