Abstract
We study the time evolution of non-Hermitian systems periodically driven by a high-frequency field. The analytical time-dependent wavefunctions can be obtained with a perturbation method. Our analytical expressions for the two-state non-Hermitian system agree very well with that of the directly numerical simulation of the evolution equation. It is shown that the probabilities of the two states will oscillate periodically for all the initial states in the real-eigenenergy phase. The system even shows an almost perfect Rabi-oscillation when both the eigenenergy of the time-independent effective Hamiltonian is real and the corresponding initial states are the eigenstates of the effective Hamiltonian. In the imaginary-eigenenergy phase, the population will grow or decay for some time in the evolution process, depending on the initial states. Interestingly and surprisingly, our results show that the probabilities will inevitably increase for the long-time evolution.
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This work was supported by the National Natural Science Foundation of China, under Grants No. 12047501.
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Zheng, GP., Wang, GT. Time Evolution of Non-Hermitian Systems Driven by a High-Frequency Field. Int J Theor Phys 61, 38 (2022). https://doi.org/10.1007/s10773-022-04989-z
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DOI: https://doi.org/10.1007/s10773-022-04989-z