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Infinite series of time-dependent Dyson maps

Fring, A. ORCID: 0000-0002-7896-7161 and Tenney, R. (2021). Infinite series of time-dependent Dyson maps. Journal of Physics A: Mathematical and Theoretical, doi: 10.1088/1751-8121/ac31a0


We propose and explore a scheme that leads to an infinite series of time-dependent Dyson maps which associate different Hermitian Hamiltonians to a uniquely specified time-dependent non-Hermitian Hamiltonian. We identify the underlying symmetries responsible for this feature respected by various Lewis-Riesenfeld invariants. The latter are used to facilitate the explicit construction of the Dyson maps and metric operators. As a concrete example for which the scheme is worked out in detail we present a two-dimensional system of oscillators that are coupled to each other in a non-Hermitian PT-symmetrical fashion.

Publication Type: Article
Additional Information: This is the Accepted Manuscript version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical.  IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.  This Accepted Manuscript is published under a CC BY-NC-ND 3.0 licence. The Version of Record is available online at
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
Date available in CRO: 26 Oct 2021 13:29
Date deposited: 26 October 2021
Date of acceptance: 20 October 2021
Date of first online publication: 20 October 2021
[img] Text - Accepted Version
This document is not freely accessible until 20 October 2022 due to copyright restrictions.
Available under License Creative Commons: Attribution-Noncommercial-No Derivative Works 3.0.

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