### Abstract

We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V± (z)=-U(z) 2 ±z(ddz)U(z) where U(z) k>0 k zk. In particular, we consider the cases generated by U(z)=z and z(1-z). We also briefly consider the effects of magnetic vector potentials on the partition functions of these systems.

Original language | English (US) |
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Article number | 092108 |

Journal | Journal of Mathematical Physics |

Volume | 48 |

Issue number | 9 |

DOIs | |

State | Published - 2007 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*48*(9), [092108]. https://doi.org/10.1063/1.2191367

**Supersymmetric biorthogonal quantum systems.** / Curtright, Thomas; Mezincescu, Alexandru; Schuster, David.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 48, no. 9, 092108. https://doi.org/10.1063/1.2191367

}

TY - JOUR

T1 - Supersymmetric biorthogonal quantum systems

AU - Curtright, Thomas

AU - Mezincescu, Alexandru

AU - Schuster, David

PY - 2007

Y1 - 2007

N2 - We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V± (z)=-U(z) 2 ±z(ddz)U(z) where U(z) k>0 k zk. In particular, we consider the cases generated by U(z)=z and z(1-z). We also briefly consider the effects of magnetic vector potentials on the partition functions of these systems.

AB - We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V± (z)=-U(z) 2 ±z(ddz)U(z) where U(z) k>0 k zk. In particular, we consider the cases generated by U(z)=z and z(1-z). We also briefly consider the effects of magnetic vector potentials on the partition functions of these systems.

UR - http://www.scopus.com/inward/record.url?scp=34848836343&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34848836343&partnerID=8YFLogxK

U2 - 10.1063/1.2191367

DO - 10.1063/1.2191367

M3 - Article

AN - SCOPUS:34848836343

VL - 48

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

M1 - 092108

ER -