Finite-gap systems, tri-supersymmetry and self-isospectrality

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dc.creatorCorrea, Francisco
dc.creatorJakubsky, Vit
dc.creatorPlyushchay, Mikhail S.
dc.date2008-06-10
dc.date2008-10-24
dc.date.accessioned2026-07-07T11:51:31Z
dc.date.available2026-07-07T11:51:31Z
dc.descriptionWe show that an n-gap periodic quantum system with parity-even smooth potential admits $2^n-1$ isospectral super-extensions. Each is described by a tri-supersymmetry that originates from a higher-order differential operator of the Lax pair and two-term nonsingular decompositions of it; its local part corresponds to a spontaneously partially broken centrally extended nonlinear N=4 supersymmetry. We conjecture that any finite-gap system having antiperiodic singlet states admits a self-isospectral tri-supersymmetric extension with the partner potential to be the original one translated for a half-period. Applying the theory to a broad class of finite-gap elliptic systems described by a two-parametric associated Lame equation, our conjecture is supported by the explicit construction of the self-isospectral tri-supersymmetric pairs. We find that the spontaneously broken tri-supersymmetry of the self-isospectral periodic system is recovered in the infinite period limit.
dc.description40 pages, published version
dc.identifierhttps://arxiv.org/abs/0806.1614
dc.identifierhttp://arxiv.org/abs/0806.1614
dc.identifierJ.Phys.A41:485303,2008
dc.identifierdoi:10.1088/1751-8113/41/48/485303
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/203927
dc.subjectHigh Energy Physics - Theory
dc.subjectOther Condensed Matter
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.subjectQuantum Physics
dc.titleFinite-gap systems, tri-supersymmetry and self-isospectrality
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