Three perspectives on entropy dynamics in a non-Hermitian two-state system
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910711492378624 |
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| author | Felski, Alexander Beygi, Alireza Karapoulitidis, Christos Klevansky, S. P. |
| author_facet | Felski, Alexander Beygi, Alireza Karapoulitidis, Christos Klevansky, S. P. |
| contents | A comparative study of entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping. In this it is demonstrated that their differences are rooted in the treatment of the environmental coupling mode. For unbroken $\mathcal{PT}$ symmetry of the system, a notable characteristic feature of the perspective taken is the presence or absence of purity oscillations, with an associated entropy revival. The description of the system is then continued from its $\mathcal{PT}$-symmetric pseudo-Hermitian phase into the regime of spontaneously broken symmetry, in the latter two approaches through a non-analytic operator-based continuation, yielding a Lindblad master equation based on the $\mathcal{PT}$ charge operator $\mathcal{C}$. This phase transition indicates a general connection between the pseudo-Hermitian closed-system and the Lindbladian open-system formalism through a spontaneous breakdown of the underlying physical reflection symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03492 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three perspectives on entropy dynamics in a non-Hermitian two-state system Felski, Alexander Beygi, Alireza Karapoulitidis, Christos Klevansky, S. P. Quantum Physics Mathematical Physics A comparative study of entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping. In this it is demonstrated that their differences are rooted in the treatment of the environmental coupling mode. For unbroken $\mathcal{PT}$ symmetry of the system, a notable characteristic feature of the perspective taken is the presence or absence of purity oscillations, with an associated entropy revival. The description of the system is then continued from its $\mathcal{PT}$-symmetric pseudo-Hermitian phase into the regime of spontaneously broken symmetry, in the latter two approaches through a non-analytic operator-based continuation, yielding a Lindblad master equation based on the $\mathcal{PT}$ charge operator $\mathcal{C}$. This phase transition indicates a general connection between the pseudo-Hermitian closed-system and the Lindbladian open-system formalism through a spontaneous breakdown of the underlying physical reflection symmetry. |
| title | Three perspectives on entropy dynamics in a non-Hermitian two-state system |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2404.03492 |