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arXiv · 1511.08092

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

Andreas Fring·Miled H. Y. Moussa
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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 non-observable operator as it ceases to be quasi-Hermitian when the metric becomes time-dependent.

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Andreas Fring, Miled H. Y. Moussa. 2015-11-25. Unitary quantum evolution for time-dependent quasi-Hermitian systems with non-observable Hamiltonians. https://doi.org/10.1103/physreva.93.042114

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