The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry

Details The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry

2009-04-17

arxiv.org/abs/0904.2768v2

Annals Phys.324:2522-2547,2009

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 4 figures; published version

Scientific paper

10.1016/j.aop.2009.06.005

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.

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