Dissipative evolution of a two-level system through a geometry-based classical mapping
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917381069078528 |
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| author | Gil, Daniel Martínez Bargueño, Pedro Miret-Artés, Salvador |
| author_facet | Gil, Daniel Martínez Bargueño, Pedro Miret-Artés, Salvador |
| contents | In this manuscript, we introduce a geometry-based formalism to obtain a Meyer-Miller-Stock-Thoss mapping in order to study the dynamics of both isolated and interacting two-level systems. After showing the description of the isolated case using canonically conjugate variables, we implement an interaction model by bilinearly coupling the corresponding population differences {\it à la} Caldeira-Leggett, showing that the dynamics behave as a Gross-Pitaevskii-like one. We also find a transition between oscillatory and tunneling-suppressed dynamics that can be observed by varying the coupling constant. After extending our model to the {\it system plus environment} case, where the environment is considered as a collection of two-level systems, we show tunneling-suppressed dynamics in the strong coupling limit and the usual damping effect similar to that of a harmonic oscillator bath in the weak coupling one. Finally, we observe that our interacting model turns an isolated symmetric two-level system into an environment-assisted asymmetric one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dissipative evolution of a two-level system through a geometry-based classical mapping Gil, Daniel Martínez Bargueño, Pedro Miret-Artés, Salvador Quantum Physics In this manuscript, we introduce a geometry-based formalism to obtain a Meyer-Miller-Stock-Thoss mapping in order to study the dynamics of both isolated and interacting two-level systems. After showing the description of the isolated case using canonically conjugate variables, we implement an interaction model by bilinearly coupling the corresponding population differences {\it à la} Caldeira-Leggett, showing that the dynamics behave as a Gross-Pitaevskii-like one. We also find a transition between oscillatory and tunneling-suppressed dynamics that can be observed by varying the coupling constant. After extending our model to the {\it system plus environment} case, where the environment is considered as a collection of two-level systems, we show tunneling-suppressed dynamics in the strong coupling limit and the usual damping effect similar to that of a harmonic oscillator bath in the weak coupling one. Finally, we observe that our interacting model turns an isolated symmetric two-level system into an environment-assisted asymmetric one. |
| title | Dissipative evolution of a two-level system through a geometry-based classical mapping |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2501.03760 |