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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
descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Dec 2009Embargo end date: 01 Jan 2009 English Publisher:Elsevier BVJournal:Annals of Physics, volume 324, pages 2,522-2,547 (issn: 0003-4916, Copyright policy )
Authors: Correa, Francisco; Dunne, Gerald V.; Plyushchay, Mikhail S.;

doi: 10.1016/j.aop.2009.06.005 , 10.48550/arxiv.0904.2768

arXiv: 0904.2768

handle: 10533/141154

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

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.

25 pages, 4 figures; published version

Related Organizations
Keywords

supersymmetric quantum mechanics, High Energy Physics - Theory, Quantum Physics, Supersymmetry and quantum mechanics, Condensed Matter - Superconductivity, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, Mathematical Physics (math-ph), Superconductivity (cond-mat.supr-con), High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), nonlinear symmetries, integrable systems, High Energy Physics - Theory (hep-th), Bogoliubov/de Gennes system, Quantum Physics (quant-ph), Mathematical Physics

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 60
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
60
Top 10%
Top 10%
Top 10%
Green
bronze