Microscopic Derivation of the Ginzburg-Landau Model

TL;DR

This paper rigorously derives the Ginzburg-Landau theory from the microscopic BCS model near the critical temperature, using semiclassical analysis with minimal regularity assumptions.

Contribution

It provides a rigorous mathematical derivation of the Ginzburg-Landau model from the BCS theory in a specific scaling limit.

Findings

Ginzburg-Landau theory emerges as an effective macroscopic model near critical temperature.

The derivation uses semiclassical analysis with minimal regularity assumptions.

The work bridges microscopic BCS theory and macroscopic Ginzburg-Landau equations.

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.