2015/11/25 by Andreas Fring, Miled H. Y. Moussa
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.93.042114
published as Phys. Rev. A 93, 042114 (2016) · 10 pages
arxiv created 2015/11/25 · arxiv updated 2016/04/27
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.