数苑经纬讲坛（124）：From Bogoliubov-de Gennes to Ginzburg-Landau: Critical Points Near Tcin the Non-Magnetic Case
来源：
发布时间：2026-11-09
报告时间：- Beijing Time: 16:00--, November 9 (Monday), 2026
- 报告地点：
- Zoom 会议号: 983 309 9626 密码: 202611
- 报告人：
- Professor Rupert L. Frank
- 报告人单位：
- LMU Munich (Germany)
- 邀请人：
- 郭玉劲
- 摘要：
- We study the relation between the Bogoliubov-de Gennes (BdG) equation and the Ginzburg-Landau (GL) equation for a BCS model without external fields. While previous rigorous derivations of GL theory from BCS theory have focused on energies and minimizers, here we consider arbitrary critical points in the relevant energy regime. For temperatures close to the critical temperature, we prove that every sufficiently small solution of the BdG equation admits an asymptotic factorization into a microscopic Cooper-pair profile and a macroscopic order parameter. The latter satisfies the GL equation up to an error that vanishes in the scaling limit. We also prove the opposite direction, going from a solution of the GL equation to an approximate solution of the BdG equation. Our analysis relies on a Birman-Schwinger reformulation of the BdG equation, a Lyapunov-Schmidt type reduction, and semiclassical estimates at low regularity. The talk is based on joint work with C. Hainzl and Dong Hao Ou Yang.
Professor Rupert L. Frank, LMU Munich (Germany)
