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Time-dependent metric for the two-dimensional, non-Hermitian coupled oscillator

Fring, A. ORCID: 0000-0002-7896-7161 & Frith, T. (2020). Time-dependent metric for the two-dimensional, non-Hermitian coupled oscillator. Modern Physics Letters A, 35(8), 2050041. doi: 10.1142/s0217732320500418

Abstract

We provide a time-dependent Dyson map and metric for the two-dimensional harmonic oscillator with a non-Hermitian ixy coupling term. This particular time-independent model exhibits spontaneously broken [Formula: see text]-symmetry and becomes unphysical in the broken regime, with the spectrum becoming partially complex. By introducing an explicit time dependence into the Dyson map, we provide a time-dependent metric that renders the model consistent across the unbroken and broken regimes.

Publication Type: Article
Additional Information: Electronic version of an article published as Fring, A. and Frith, T. (2020). Time-dependent metric for the two-dimensional, non-Hermitian coupled oscillator. Modern Physics Letters A, 35(8), 2050041, https://doi.org/10.1142/S0217732320500418 © World Scientific Publishing Company, https://www.worldscientific.com/worldscinet/mpla.
Publisher Keywords: Quantum mechanics, PT symmetry, non-Hermitian
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
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