Mending the broken PT-regime via an explicit time-dependent Dyson map

Fring, A. & Frith, T. (2017). Mending the broken PT-regime via an explicit time-dependent Dyson map. Physics Letters A, 381(29), pp. 2318-2323. doi: 10.1016/j.physleta.2017.05.041

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Abstract

We demonstrate that non-Hermitian Hamiltonian systems with spontaneously broken PT-symmetry and partially complex eigenvalue spectrum can be made meaningful in a quantum mechanical sense when introducing some explicit time-dependence into their parameters. Exploiting the fact that explicitly time-dependent non-Hermitian Hamiltonians are unobservable and not identical to the energy operators in such a scenario, we show that their corresponding non-Hermitian energy operators develop a different type of PT-symmetry from the Hamiltonians that ensures the reality of their energy spectra. For this purpose we analytically solve the fully time-dependent Dyson equation with all quantities involved being explicitly time-dependent giving rise to a time-dependent metric. The key auxiliary equation to be solved for the two level atomic system considered here is the nonlinear Ermakov–Pinney equation with time-dependent coefficients.

Item Type: Article
Additional Information: © 2017, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords: PT-symmetric quantum mechanics; Non-Hermitian quantum mechanics; Time-dependent Hamiltonian systems
Subjects: Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/17500

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