Microscopic Derivation of Ginzburg-Landau Theory
Mathematical Physics
2012-05-28 v1 Quantum Gases
Superconductivity
math.MP
Spectral Theory
Abstract
We give the first 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.
Keywords
Cite
@article{arxiv.1102.4001,
title = {Microscopic Derivation of Ginzburg-Landau Theory},
author = {Rupert L. Frank and Christian Hainzl and Robert Seiringer and Jan Philip Solovej},
journal= {arXiv preprint arXiv:1102.4001},
year = {2012}
}
Comments
44 pages