期刊
PHYSICS LETTERS A
卷 381, 期 29, 页码 2318-2323出版社
ELSEVIER
DOI: 10.1016/j.physleta.2017.05.041
关键词
PT-symmetric quantum mechanics; Non-Hermitian quantum mechanics; Time-dependent Hamiltonian systems
资金
- City, University of London Research Fellowship
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. (C) 2017 Elsevier B.V. All rights reserved.
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