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

Andreas Fring

Department of Mathematics, City, University of London, Northampton Square, London EC1V 0HB, UK

E-mail Address: a.fring@city.ac.uk

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and

Thomas Frith

Department of Mathematics, City, University of London, Northampton Square, London EC1V 0HB, UK

E-mail Address: thomas.frith@city.ac.uk

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https://doi.org/10.1142/S0217732320500418Cited by:11 (Source: Crossref)

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 $𝒫 𝒯$ -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.

Keywords:

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