Self-isospectral tri-supersymmetry in -symmetric quantum systems with pure imaginary periodicity

详细信息	查看全文 | 推荐本文 |

• 作者：Francisco Correa^a ; ^{correa@cecs.cl} ; Mikhail S. Plyushchay^b ; ^{mikhail.plyushchay@usach.cl}
• 关键词：Supersymmetric quantum mechanics ; PT-symmetry ; Non-Hermitian Hamiltonian ; Self-isospectrality ; Finite-gap system ; Non-linear supersymmetry
• 刊名：Annals of Physics
• 出版年：2012
• 期刊代码：63_00034916
• 类别：mt
• 出版时间：June, 2012
• 卷：327
• 期：6
• 页码：1761-1783
• 文件大小：471 K

摘要

We study a reflectionless -symmetric quantum system described by the pair of complexified Scarf II potentials mutually displaced in the half of their pure imaginary period. Analyzing the rich set of intertwining discrete symmetries of the pair, we find an exotic supersymmetric structure based on three matrix differential operators that encode all the properties of the system, including its reflectionless (finite-gap) nature. The structure we revealed particularly sheds new light on the splitting of the discrete states into two families, related to the bound and resonance states in Hermitian Scarf II counterpart systems, on which two different series of irreducible representations of are realized.