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

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 solve...

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Bibliographic Details
Published inarXiv.org
Main Authors Fring, Andreas, Moussa, Miled H Y
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.11.2015
Subjects
Evolution
Physics - Quantum Physics
Time dependence
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1511.08092