Supersymmetric biorthogonal quantum systems

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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 languageEnglish (US)
Article number092108
JournalJournal of Mathematical Physics
Volume48
Issue number9
DOIs
StatePublished - Oct 8 2007

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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