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Cooperative Emission of Radiation as a Subordinated Random Process

  • ATOMS, MOLECULES, OPTICS
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Abstract

Collective emission of radiation by two-level impurities in a complex dielectric medium is represented as a subordinated random process controlled by an alpha-stable process with parameter α determined by characteristic radiation damping times. The differences from conventional superradiance are determined. Physical foundations used for introducing subordination can also be useful for other radiation problems.

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Notes

  1. Function Mα(z) is nonnegative for z ≥ 0 and normalizable, \(\int_0^\infty {{{M}_{\alpha }}} \)(z)dz = 1, with Laplace transform \(\mathcal{L}\)(Mα(t, s)) = Eα, 1(–s). For 0 < α ≤ 1/2, it decreases monotonically, while for 1/2 < α < 1, it has a maximum at a certain point depending on α. In addition M1(z) = δ(z – 1), M1, 2(z) = \({{\pi }^{{ - 1/2}}}{\text{exp}}\left( { - \frac{{{{z}^{2}}}}{4}} \right),\) M1/3(z) = \({{3}^{{2/3}}}{\text{Ai}}\left( {\frac{z}{{{{3}^{1}}{\text{/}}3}}} \right),\) Ai(z) being the Airy function.

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Funding

This study was supported in part by the Russian Foundation for Basic Research (project no. 19-02-00234a).

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Authors and Affiliations

  1. Russian Research Center “Kurchatov Institute”, 123182, Moscow, Russia

    A. M. Basharov

  2. Moscow Institute of Physics and Technology, 141701, Dolgoprudny, Moscow oblast, Russia

    A. M. Basharov

  3. St. Petersburg University of State Fire Services of EMERCOM of Russia, 196105, St. Petersburg, Russia

    A. I. Trubilko

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  1. A. M. Basharov
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Correspondence to A. M. Basharov or A. I. Trubilko.

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Translated by N. Wadhwa

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Basharov, A.M., Trubilko, A.I. Cooperative Emission of Radiation as a Subordinated Random Process. J. Exp. Theor. Phys. 133, 143–153 (2021). https://doi.org/10.1134/S106377612108001X

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