Fake supersymmetry with tadpole potentials

Supersymmetry Breaking with Periodic Potentials

We discuss supersymmetry breaking in some supersymmetric quantum mechanical models with periodic potentials. The sensitivity to the parameters appearing in the superpotential is more acute than in conventional nonperiodic models. We present some simple elliptic models to illustrate these points. Supersymmetry (SUSY) breaking is an outstanding problem that is directly relevant for the applicatio...

Periodic Potentials and Supersymmetry

We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of analytically solvable one-dimensional periodic potentials. Further, using the Landen transformations as well as cyclic identities for Jacobi elliptic functions discove...

Supersymmetry-generated complex optical potentials with real spectra

We show that the formalism of supersymmetry (SUSY), when applied to parity-time (PT ) symmetric optical potentials, can give rise to refractive index landscapes with altogether nontrivial properties. In particular, we find that the presence of gain and loss allows for arbitrarily removing bound states from the spectrum of a structure. This is in stark contrast to the Hermitian case, where the S...

Supersymmetry and Schrödinger-type operators with distributional matrix-valued potentials

Building on work on Miura’s transformation by Kappeler, Perry, Shubin, and Topalov, we develop a detailed spectral theoretic treatment of Schrödinger operators with matrix-valued potentials, with special emphasis on distributional potential coefficients. Our principal method relies on a supersymmetric (factorization) formalism underlying Miura’s transformation, which intimately connects the tri...

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