Federico Girotti
Large deviations, central limit, and dynamical phase transitions in the atom maser
Girotti, Federico; Van Horssen, Merlijn; Carbone, Raffaella; Guţa, Madalin
Authors
Merlijn Van Horssen
Raffaella Carbone
Dr MADALIN GUTA madalin.guta@nottingham.ac.uk
ASSOCIATE PROFESSOR
Contributors
Dr MADALIN GUTA madalin.guta@nottingham.ac.uk
Researcher
Abstract
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 crossover rather than a genuine phase transition. We argue, however, that the latter occurs in the limit of an 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 Gärtner-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.
Citation
Girotti, F., Van Horssen, M., Carbone, R., & Guţa, M. (2022). Large deviations, central limit, and dynamical phase transitions in the atom maser. Journal of Mathematical Physics, 63(6), Article 062202. https://doi.org/10.1063/5.0078916
Journal Article Type | Article |
---|---|
Acceptance Date | May 15, 2022 |
Online Publication Date | Jun 8, 2022 |
Publication Date | Jun 1, 2022 |
Deposit Date | Jun 13, 2022 |
Publicly Available Date | Jun 14, 2022 |
Journal | Journal of Mathematical Physics |
Print ISSN | 0022-2488 |
Electronic ISSN | 1089-7658 |
Publisher | American Institute of Physics |
Peer Reviewed | Peer Reviewed |
Volume | 63 |
Issue | 6 |
Article Number | 062202 |
DOI | https://doi.org/10.1063/5.0078916 |
Keywords | Mathematical Physics; Statistical and Nonlinear Physics |
Public URL | https://nottingham-repository.worktribe.com/output/8493273 |
Publisher URL | https://aip.scitation.org/doi/10.1063/5.0078916 |
Files
Large Deviations Central Limit And Dynamical Phase Transitions In The Atom Maser
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Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/
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