Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry

TL;DR

This paper explores the complex supersymmetric structures of a self-isospectral Poschl-Teller system, revealing exotic nonlinear supersymmetry, mirror symmetry, and connections to Dirac and Bogoliubov-de Gennes systems through Darboux transformations.

Contribution

It uncovers new exotic nonlinear supersymmetry features and multiple grading operators in a self-isospectral Poschl-Teller system, linking it to Dirac and Bogoliubov-de Gennes models.

Findings

Identification of a partially broken nonlinear supersymmetry.

Existence of seven grading operator options.

Connection of supersymmetry generators to free particle integrals.

Abstract

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. We find that the supersymmetry generators for the both systems are the Darboux-dressed integrals of a free spin-1/2 particle in the Schrodinger picture, or of a free massive Dirac particle. Nonlocal Foldy- Wouthuysen transformations are shown to be involved in the supersymmetric structure.