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arXiv · 1812.02862

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

Andreas Fring·Thomas Frith
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Abstract

We provide a time-dependent Dyson map and metric for the two dimensional harmonic oscillator with a non-Hermitian $i xy$ coupling term. This particular time-independent model exhibits spontaneously broken $\mathcal{PT}$-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.

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Andreas Fring, Thomas Frith. 2018-12-07. Time-dependent metric for the two dimensional, non-Hermitian coupled oscillator. https://doi.org/10.1142/s0217732320500418

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