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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.24437 |
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| _version_ | 1866917398861316096 |
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| author | Alvarez, Yanet Portesi, Mariela Ramirez, Romina Reboiro, Marta |
| author_facet | Alvarez, Yanet Portesi, Mariela Ramirez, Romina Reboiro, Marta |
| contents | We investigate uncertainty relations for quantum observables evolving under non-Hermitian Hamiltonians, with particular emphasis on the role of metric operators. By constructing appropriate metrics in each dynamical regime, namely the unbroken-symmetry phase, the spontaneously broken-symmetry phase, and at exceptional points, we provide a consistent definition of expectation values, variances, and time evolution within a Krein-space framework. Within this approach, we derive a generalized Heisenberg-Robertson uncertainty inequality which is valid across all spectral regimes. As an application, we analyze a spin model with parity-time reversal symmetry and show that, while the uncertainty measure exhibits oscillatory behavior in the unbroken phase, it evolves towards a minimum-uncertainty steady state in the spontaneously broken-symmetry phase and at exceptional points. We further compare our metric-based description with a Lindblad master-equation approach and show their agreement in the steady state. Our results highlight the necessity of incorporating appropriate metric structures to extract physically meaningful predictions from non-Hermitian quantum dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uncertainty inequalities in a non-Hermitian scenario Alvarez, Yanet Portesi, Mariela Ramirez, Romina Reboiro, Marta Quantum Physics We investigate uncertainty relations for quantum observables evolving under non-Hermitian Hamiltonians, with particular emphasis on the role of metric operators. By constructing appropriate metrics in each dynamical regime, namely the unbroken-symmetry phase, the spontaneously broken-symmetry phase, and at exceptional points, we provide a consistent definition of expectation values, variances, and time evolution within a Krein-space framework. Within this approach, we derive a generalized Heisenberg-Robertson uncertainty inequality which is valid across all spectral regimes. As an application, we analyze a spin model with parity-time reversal symmetry and show that, while the uncertainty measure exhibits oscillatory behavior in the unbroken phase, it evolves towards a minimum-uncertainty steady state in the spontaneously broken-symmetry phase and at exceptional points. We further compare our metric-based description with a Lindblad master-equation approach and show their agreement in the steady state. Our results highlight the necessity of incorporating appropriate metric structures to extract physically meaningful predictions from non-Hermitian quantum dynamics. |
| title | Uncertainty inequalities in a non-Hermitian scenario |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.24437 |