Non-Hermitian Quantum Fermi Accelerator
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929281721958400 |
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| author | Fring, Andreas Taira, Takano |
| author_facet | Fring, Andreas Taira, Takano |
| contents | 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 depletion 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07950 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian Quantum Fermi Accelerator Fring, Andreas Taira, Takano Quantum Physics Mathematical Physics 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 depletion 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. |
| title | Non-Hermitian Quantum Fermi Accelerator |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2304.07950 |