Large Emission Regime in Mean Field Luminescence

TL;DR

This paper analyzes rare large emission events in a stochastic model of luminescence involving many particles, using large deviations theory to understand the probability and optimal trajectories of intense photon emission.

Contribution

It introduces a large emission regime analysis for a particle-based luminescence model and characterizes the stability of excited particle share under parameter changes.

Findings

Probability asymptotics for large photon emission events

Identification of stable excited particle share in large emission regime

Derivation of optimal trajectories for rare emission events

Abstract

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.