Reduced dynamics in quasi-Hermitian systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912744292220928 |
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| author | Badhani, Himanshu Chandrashekar, C. M. |
| author_facet | Badhani, Himanshu Chandrashekar, C. M. |
| contents | Evolutions under non-Hermitian Hamiltonians with unbroken $\mathcal{PT}$ symmetry can be considered unitary under appropriate choices of inner products, facilitated by the so-called metric operator. While it is understood that the choice of the metric operator has no bearing on the description of the system, in this work, we show that this choice does dictate the entanglement structure of the system. We show that the partial trace of the Hermitized density matrix gives the correct representation of the reduced subsystem, and based on such operations, we elucidate the metric dependency of the reduced dynamics and consequently the observable dependence of the subsystem decomposition. We use a non-Hermitian $\mathcal{PT}$-symmetric quantum walk as a toy model to study this metric dependency, where we use the internal (coin state) as the subsystem of interest and study the coin-position entanglement and non-Markovianity of the coin dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03042 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reduced dynamics in quasi-Hermitian systems Badhani, Himanshu Chandrashekar, C. M. Quantum Physics Evolutions under non-Hermitian Hamiltonians with unbroken $\mathcal{PT}$ symmetry can be considered unitary under appropriate choices of inner products, facilitated by the so-called metric operator. While it is understood that the choice of the metric operator has no bearing on the description of the system, in this work, we show that this choice does dictate the entanglement structure of the system. We show that the partial trace of the Hermitized density matrix gives the correct representation of the reduced subsystem, and based on such operations, we elucidate the metric dependency of the reduced dynamics and consequently the observable dependence of the subsystem decomposition. We use a non-Hermitian $\mathcal{PT}$-symmetric quantum walk as a toy model to study this metric dependency, where we use the internal (coin state) as the subsystem of interest and study the coin-position entanglement and non-Markovianity of the coin dynamics. |
| title | Reduced dynamics in quasi-Hermitian systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2309.03042 |