Supersymmetric biorthogonal quantum systems

Research output: Contribution to journalArticle

14 Citations (Scopus)

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 - 2007

Fingerprint

Biorthogonal System
Quantum Systems
Periodic Solution
Spectral Singularities
Associated Polynomials
Vector Potential
Partition Function
partitions
polynomials
Model

ASJC Scopus subject areas

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

Cite this

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

In: Journal of Mathematical Physics, Vol. 48, No. 9, 092108, 2007.

Research output: Contribution to journalArticle

@article{717387c1988c4d58b8fbfbb18dcd5da7,
title = "Supersymmetric biorthogonal quantum systems",
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.",
author = "Thomas Curtright and Alexandru Mezincescu and David Schuster",
year = "2007",
doi = "10.1063/1.2191367",
language = "English (US)",
volume = "48",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics Publising LLC",
number = "9",

}

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 -