Markovianity and non-Markovianity of Particle Bath with Dirac Dispersion Relation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917541034590208 |
|---|---|
| author | Taira, Takano Hatano, Naomichi Nishino, Akinori |
| author_facet | Taira, Takano Hatano, Naomichi Nishino, Akinori |
| contents | The dynamics of a two-level system coupled to a particle bath with the Dirac dispersion relation is studied. We analytically show that closing the Dirac gap results in a transition of the survival probability of the two-level system from non-exponential to exponential decay in the long-time regime, while the short-time regime remains exponential. The exact time-evolving state is also calculated. With the Dirac gap closing smoothly, the time-evolving state converges to a time-evolving resonant state, which is normalizable due to causality. We numerically show that introducing a finite cutoff to the Dirac dispersion relation leads to a transition from exponential to non-exponential decay both in short- and long-time regimes, with the time-evolving resonant state resolved to a time-evolving state. Furthermore, we propose several experimental setups that act as a particle bath with the Dirac dispersion relation. We give a detailed calculation for one of them, namely an optical array in the Su-Schrieffer-Heeger configuration. In this case, we show that our theoretical results can be observed experimentally with realistic parameters in an existing experimental setup of an optical waveguide array. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17436 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Markovianity and non-Markovianity of Particle Bath with Dirac Dispersion Relation Taira, Takano Hatano, Naomichi Nishino, Akinori Quantum Physics Mathematical Physics The dynamics of a two-level system coupled to a particle bath with the Dirac dispersion relation is studied. We analytically show that closing the Dirac gap results in a transition of the survival probability of the two-level system from non-exponential to exponential decay in the long-time regime, while the short-time regime remains exponential. The exact time-evolving state is also calculated. With the Dirac gap closing smoothly, the time-evolving state converges to a time-evolving resonant state, which is normalizable due to causality. We numerically show that introducing a finite cutoff to the Dirac dispersion relation leads to a transition from exponential to non-exponential decay both in short- and long-time regimes, with the time-evolving resonant state resolved to a time-evolving state. Furthermore, we propose several experimental setups that act as a particle bath with the Dirac dispersion relation. We give a detailed calculation for one of them, namely an optical array in the Su-Schrieffer-Heeger configuration. In this case, we show that our theoretical results can be observed experimentally with realistic parameters in an existing experimental setup of an optical waveguide array. |
| title | Markovianity and non-Markovianity of Particle Bath with Dirac Dispersion Relation |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2406.17436 |