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Large deviations, central limit, and dynamical phase transitions in the atom maser

Girotti, Federico; Van Horssen, Merlijn; Carbone, Raffaella; Gu?a, Madalin


Merlijn Van Horssen

Raffaella Carbone



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.


Girotti, F., Van Horssen, M., Carbone, R., & Gu?a, M. (2022). Large deviations, central limit, and dynamical phase transitions in the atom maser. Journal of Mathematical Physics, 63(6), Article 062202.

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
Keywords Mathematical Physics; Statistical and Nonlinear Physics
Public URL
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