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Perturbative approach for strong and weakly coupled time-dependent for non-Hermitian quantum systems

Fring, A. ORCID: 0000-0002-7896-7161 & Tenney, R. (2021). Perturbative approach for strong and weakly coupled time-dependent for non-Hermitian quantum systems. Physica Scripta, 96(4), article number 045211. doi: 10.1088/1402-4896/abe259


We propose a perturbative approach to determine the time-dependent Dyson map and the metric operator associated with time-dependent non-Hermitian Hamiltonians. We apply the method to a pair of explicitly time-dependent two dimensional harmonic oscillators that are weakly coupled to each other in a PT-symmetric fashion and to the strongly coupled explicitly time-dependent negative quartic anharmonic oscillator potential. We demonstrate that once the perturbative Ansatz is set up the coupled differential equations resulting order by order may be solved recursively in a constructive manner, thus bypassing the need for making any guess for the Dyson map or the metric operator. Exploring the ambiguities in the solutions of the order by order differential equations naturally leads to a whole set of inequivalent solutions for the Dyson maps and metric operators implying different physical behaviour as demonstrated for the expectation values of the time-dependent energy operator.

Publication Type: Article
Additional Information: This is the Accepted Manuscript version of an article accepted for publication in Physica Scripta. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
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