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Theoretical and Mathematical Physics

, Volume 198, Issue 1, pp 118–128 | Cite as

Large Fluctuations in Two-Level Systems With Stimulated Emission

  • E. A. Pechersky
  • S. A. Pirogov
  • G. M. Schütz
  • A. A. Vladimirov
  • A. A. YambartsevEmail author
Article
  • 11 Downloads

Abstract

We consider a system of N identical independent Markov processes, each taking values 0 or 1. The system describes the stochastic dynamics of an ensemble of two-level atoms. The atoms are exposed to a photon flux. Under the photon flux action, each atom changes its state with some rates either from its ground state (state 0) to the excited state (state 1) or from the excited state to the ground state (stimulated emission). The atom can also spontaneously change its state from the excited to the ground state. We study rare events where a large cumulative emission occurs during a fixed time interval [0, T]. For this, we apply the large-deviation theory, which allows an asymptotic analysis as N → ∞.

Keywords

continuous-timeMarkov process large deviation infinitesimal generator Hamiltonian Hamiltonian system 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • E. A. Pechersky
    • 1
  • S. A. Pirogov
    • 1
  • G. M. Schütz
    • 2
  • A. A. Vladimirov
    • 1
  • A. A. Yambartsev
    • 3
    Email author
  1. 1.Institute for Information Transmission ProblemsMoscowRussia
  2. 2.Interdisziplinäres Zentrum für Komplexe SystemeUniversität BonnBonnGermany
  3. 3.Institute of Mathematics and StatisticsUniversity of São Paulo (USP)São PauloBrazil

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