Supersymmetric Biorthogonal Quantum Systems
量子物理
2008-11-26 v2 高能物理 - 理论
数学物理
math.MP
摘要
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(d/(dz))U(z) where U(z) = \sum_{k>0}u_{k}z^{k}. 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.
引用
@article{arxiv.quant-ph/0603170,
title = {Supersymmetric Biorthogonal Quantum Systems},
author = {Thomas Curtright and Luca Mezincescu and David Schuster},
journal= {arXiv preprint arXiv:quant-ph/0603170},
year = {2008}
}
备注
Changes are made to conform to the published version. In particular, some errors are corrected on pp 12-13