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Non-Hermitian quantum Fermi accelerator

Fring, A. ORCID: 0000-0002-7896-7161 & Taira, T. (2023). Non-Hermitian quantum Fermi accelerator. Physical Review A, 108(1), article number 012222. doi: 10.1103/physreva.108.012222


We exactly solve a quantum Fermi accelerator model consisting of a time-independent non-Hermitian Hamiltonian with time-dependent Dirichlet boundary conditions. A Hilbert space for such systems can be defined in two equivalent ways, either by first constructing a time-independent Dyson map and subsequently unitarily mapping to fixed boundary conditions or by first unitarily mapping to fixed boundary conditions followed by the construction of a time-dependent Dyson map. In turn this allows to construct time-dependent metric operators from a time-independent metric and two time-dependent unitary maps that freeze the moving boundaries. From the time-dependent energy spectrum, we find the known possibility of oscillatory behavior in the average energy in the PT-regime, whereas in the spontaneously broken PT-regime we observe the new feature of a one-time de- pletion of the energy. We show that the PT broken regime is mended with moving boundary, equivalently to mending it with a time-dependent Dyson map.

Publication Type: Article
Additional Information: This article has been published in Physical Review A by American Physical Society, doi: 10.1103/physreva.108.012222
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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