Large Deviations, Central Limit and dynamical phase transitions in the atom maser
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2012
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| _version_ | 1866909226057596928 |
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| author | Girotti, Federico van Horssen, Merlijn Carbone, Raffaella Guta, Madalin |
| author_facet | Girotti, Federico van Horssen, Merlijn Carbone, Raffaella Guta, Madalin |
| contents | The theory of quantum jump trajectories provides a new framework for understanding dynamical phase transitions in open systems. A candidate for such transitions is the atom maser, which for certain parameters exhibits strong intermittency in the atom detection counts, and has a bistable stationary state. Although previous numerical results suggested that the "free energy" may not be a smooth function, we show that the atom detection counts satisfy a large deviations principle, and therefore we deal with a phase cross-over rather than a genuine phase transition. We argue however that the latter occurs in the limit of infinite pumping rate. As a corollary, we obtain the Central Limit Theorem for the counting process.
The proof relies on the analysis of a certain deformed generator whose spectral bound is the limiting cumulant generating function. The latter is shown to be smooth, so that a large deviations principle holds by the Gartner-Ellis Theorem. One of the main ingredients is the Krein-Rutman theory which extends the Perron-Frobenius theorem to a general class of positive compact semigroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1206_4956 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Large Deviations, Central Limit and dynamical phase transitions in the atom maser Girotti, Federico van Horssen, Merlijn Carbone, Raffaella Guta, Madalin Quantum Physics Mathematical Physics The theory of quantum jump trajectories provides a new framework for understanding dynamical phase transitions in open systems. A candidate for such transitions is the atom maser, which for certain parameters exhibits strong intermittency in the atom detection counts, and has a bistable stationary state. Although previous numerical results suggested that the "free energy" may not be a smooth function, we show that the atom detection counts satisfy a large deviations principle, and therefore we deal with a phase cross-over rather than a genuine phase transition. We argue however that the latter occurs in the limit of infinite pumping rate. As a corollary, we obtain the Central Limit Theorem for the counting process. The proof relies on the analysis of a certain deformed generator whose spectral bound is the limiting cumulant generating function. The latter is shown to be smooth, so that a large deviations principle holds by the Gartner-Ellis Theorem. One of the main ingredients is the Krein-Rutman theory which extends the Perron-Frobenius theorem to a general class of positive compact semigroups. |
| title | Large Deviations, Central Limit and dynamical phase transitions in the atom maser |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/1206.4956 |