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Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators

Fring, A. ORCID: 0000-0002-7896-7161 and Tenney, R. (2020). Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators. Physics Letters A, 384(21), 126530.. doi: 10.1016/j.physleta.2020.126530

Abstract

We construct a time-dependent double well potential as an exact spectral equivalent to the explicitly time-dependent negative quartic oscillator with a time-dependent mass term. Defining the unstable anharmonic oscillator Hamiltonian on a contour in the lower-half complex plane, the resulting time-dependent non-Hermitian Hamiltonian is first mapped by an exact solution of the time-dependent Dyson equation to a time-dependent Hermitian Hamiltonian defined on the real axis. When unitary transformed, scaled and Fourier transformed we obtain a time-dependent double well potential bounded from below. All transformations are carried out non-perturbatively so that all Hamiltonians in this process are spectrally exactly equivalent in the sense that they have identical instantaneous energy eigenvalue spectra.

Publication Type: Article
Additional Information: © 2020 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: Non-Hermitian quantum mechanics, Anharmonic oscillators, Double wells-symmetric quantum mechanics
Subjects: Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
Date Deposited: 14 May 2020 16:18
URI: https://openaccess.city.ac.uk/id/eprint/24187
[img] Text - Accepted Version
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