Stochastic Dynamics of Einstein Matter-Radiation Model with Spikes

TL;DR

This paper revises a classical matter-radiation dynamical system to include stochastic effects, analyzing spike phenomena in photon emission through Markovian processes in various limits.

Contribution

It introduces a stochastic model of matter-radiation dynamics with spikes, extending the classical Einstein model by incorporating randomness and analyzing its behavior in different regimes.

Findings

The stochastic model exhibits spike-like photon emission patterns.

In the one-component limit, the process is a positive recurrent Markov chain.

The model's behavior is characterized in many-component, mean-field, and one-component limits.

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.