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

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

2008-06-10

arxiv.org/abs/0806.1614v3

J.Phys.A41:485303,2008

Physics

High Energy Physics

High Energy Physics - Theory

40 pages, published version

Scientific paper

10.1088/1751-8113/41/48/485303

We 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.

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