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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2504.02050 |
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| _version_ | 1866914600556953600 |
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| author | da Silva, L. F. Alves Moussa, M. H. Y. |
| author_facet | da Silva, L. F. Alves Moussa, M. H. Y. |
| contents | Here we first present an alternative formulation of the Lewis & Riesenfeld theorem for solving the Schrödinger equation with nonautonomous Hermitian and pseudo-Hermitian Hamiltonians. We then employ this framework to characterize the spontaneous breaking of time-dependent antilinear symmetries of these Hamiltonians. We demonstrate that, under unbroken antilinear symmetries, the Lewis & Riesenfeld phases are real and odd functions of time, which allows us to recover the well-known real spectra of time-independent pseudo-Hermitian Hamiltonians. However, in the spontaneously broken regime, imaginary components of the Lewis & Riesenfeld phases arise, leading to coalescence effects analogous to those in the time-independent scenario. Finally, we present an illustrative example of unbroken and broken PT-symmetry for a time-dependent Hamiltonian modeling the non-Hermitian dynamical Casimir effect. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spontaneous symmetry breaking for nonautonomous pseudo-Hermitian systems da Silva, L. F. Alves Moussa, M. H. Y. Quantum Physics Here we first present an alternative formulation of the Lewis & Riesenfeld theorem for solving the Schrödinger equation with nonautonomous Hermitian and pseudo-Hermitian Hamiltonians. We then employ this framework to characterize the spontaneous breaking of time-dependent antilinear symmetries of these Hamiltonians. We demonstrate that, under unbroken antilinear symmetries, the Lewis & Riesenfeld phases are real and odd functions of time, which allows us to recover the well-known real spectra of time-independent pseudo-Hermitian Hamiltonians. However, in the spontaneously broken regime, imaginary components of the Lewis & Riesenfeld phases arise, leading to coalescence effects analogous to those in the time-independent scenario. Finally, we present an illustrative example of unbroken and broken PT-symmetry for a time-dependent Hamiltonian modeling the non-Hermitian dynamical Casimir effect. |
| title | Spontaneous symmetry breaking for nonautonomous pseudo-Hermitian systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.02050 |