Unitary quantum evolution for time-dependent quasi-Hermitian systems with nonobservable Hamiltonians

Fring, A. & Moussa, M. (2016). Unitary quantum evolution for time-dependent quasi-Hermitian systems with nonobservable Hamiltonians. Physical review. A, General physics, 93, 042114. doi: 10.1103/PhysRevA.93.042114

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Abstract

It has been argued that it is incompatible to maintain unitary time evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time dependent. We demonstrate here that the time-dependent Dyson equation and the time-dependent quasi-Hermiticity relation can be solved consistently in such a scenario for a time-dependent Dyson map and time-dependent metric operator, respectively. These solutions are obtained at the cost of rendering the non-Hermitian Hamiltonian to be a nonobservable operator as it ceases to be quasi-Hermitian when the metric becomes time dependent.

Item Type: Article
Additional Information: Copyright American Physical Society 2016
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/14468

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