Microscopic Derivation of the Ginzburg-Landau Model

Abstract

We present a summary of our recent rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof.

Typo in Eq. (14) corrected, references updated

References in corpus (2)

• Critical Temperature and Energy Gap for the BCS Equation
• Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs

Cited by in corpus (3)

• The external field dependence of the BCS critical temperature
• On the Bogolubov-de Gennes Equations
• Differential Equations of Quantum Mechanics