Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry

Understand

We study supersymmetry of a self-isospectral one-gap Poschl-Teller system in the light of a mirror symmetry that is based on spatial and shift reflections.

• The revealed exotic, partially broken nonlinear supersymmetry admits seven alternatives for a grading operator.
• One of its local, first order supercharges may be identified as a Hamiltonian of an associated one-gap, non-periodic Bogoliubov-de Gennes system.
• The latter possesses a nonlinear supersymmetric structure, in which any of the three non-local generators of a Clifford algebra may be chosen as the grading operator.