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Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems

Cen, J., Fring, A. ORCID: 0000-0002-7896-7161 and Frith, T. (2019). Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems. Journal of Physics A: Mathematical and Theoretical, doi: 10.1088/1751-8121/ab0335

Abstract

We propose time-dependent Darboux (supersymmetric) transformations that provide a scheme for the calculation of explicitly time-dependent solvable non-Hermitian partner Hamiltonians. Together with two Hermitian Hamilitonians the latter form a quadruple of Hamiltonians that are related by two time-dependent Dyson equations and two intertwining relations in form of a commutative diagram. Our construction is extended to the entire hierarchy of Hamiltonians obtained from time-dependent Darboux-Crum transformations. 
 As an alternative approach we also discuss the intertwining relations for Lewis-Riesenfeld invariants for Hermitian as well as non-Hermitian Hamiltonians that reduce the time-dependent equations to auxiliary eigenvalue equations. The working of our proposals is discussed for a hierarchy of explicitly time-dependent rational, hyperbolic, Airy function and nonlocal potentials.

Publication Type: Article
Additional Information: © 2018 IOP Publishing Ltd. This Accepted Manuscript is available for reuse under a CC BY-NC-ND 3.0 licence after the 12 month embargo period provided that all the terms of the licence are adhered to.
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/21407
[img] Text - Accepted Version
This document is not freely accessible until 30 January 2020 due to copyright restrictions.
Available under License Creative Commons: Attribution-Noncommercial-No Derivative Works 3.0.

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