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arXiv · 1803.08962

Stochastic Dynamics of Einstein Matter-Radiation Model with Spikes

E. Pechersky·A. Yambartsev·V. Zagrebnov
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Abstract

Motivated by the Einstein classical description of the matter-radiation dynamics we revise a dynamical system producing spikes of the photon emission. Then we study the corresponding stochastic model, which takes into account the randomness of spontaneous and stimulated atomic transitions supporting by a pumping. Our model reduces to Markovian density dependent processes for the inversion coefficient and the photon specific value driven by small but fast jumps. We analyse the model in three limits: the many-component, the mean-field, and the one-component. In the last case it is a positive recurrent Markov chain with sound spikes.

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E. Pechersky, A. Yambartsev, V. Zagrebnov. 2018-03-23. Stochastic Dynamics of Einstein Matter-Radiation Model with Spikes. https://arxiv.org/abs/1803.08962

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