# Moscow Mathematical Journal

Volume 19, Issue 1, January–March 2019 pp. 107–120.

Large Emission Regime in Mean Field Luminescence

**Authors**:
E. Pechersky (1), S. Pirogov (1), G. M. Schütz (2), A. Vladimirov (1), and A. Yambartsev (3)

**Author institution:**(1) Institute for Information Transmission Problems, 19, Bol. Karetny, Moscow, 127994, Russia

(2) Interdisziplinäres Zentrum für Komplexe Systeme, Universität Bonn, Brühler Str. 7, 53119 Bonn, Germany

(3) Institute of Mathematics and Statistics, University of São Paulo (USP), Sãao Paulo 05508-090, SP, Brazil

**Summary: **

We study a class of random processes on *N* particles which
can be interpreted as stochastic model of luminescence. Each particle
can stay in one of two states: Excited state or ground state. Any particle
at ground state is excited with a constant rate (pumping). The number of excited particles decreases by means of photon emission through
interactions of the particles. We analyse the rare event of flashes, i.e.,
the emission of a very large number of photons *B* during a fixed time
interval *T*. We employ the theory of large deviations to provide the
asymptotics of the probability of such event when the total number of
particles *N* tends to infinity. This theory gives us also the optimal trajectory of scaled process corresponding to this event. The stationary
regime of this process we call the large emission regime. In several cases
we prove that in the large emission regime a share of excited particles in
a system is stable under the changes of the pumping and emission rates.

2010 Math. Subj. Class. Primary: 60J, 60F10; Secondary: 60K35.

**Keywords:**Continuous-time Markov processes, large deviations, infinitesimal generator, Hamiltonian, Hamiltonian system.

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