arXiv:0904.2768·v2·High Energy Physics — Theory
The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry
Francisco Correa🇨🇱 · Gerald V. Dunne🇺🇸 · Mikhail S. Plyushchay🇨🇱
Abstract
We show that the Ginzburg-Landau expansion of the grand potential for the Bogoliubov-de Gennes Hamiltonian is determined by the integrable nonlinear equations of the AKNS hierarchy, and that this provides the natural mathematical framework for a hidden nonlinear quantum mechanical supersymmetry underlying the dynamics.
Comments: 25 pages, 4 figures; published version