# Large Fluctuations of Radiation in Stochastically Activated Two-Level Systems

## TL;DR

This paper investigates the probability and dynamics of large radiation fluctuations in a system of many non-interacting two-level atoms, revealing that during large fluctuations about half of the atoms tend to be excited regardless of stationary state conditions.

## Contribution

It introduces two methods—large deviation principles and a quantum formalism analogue—for analyzing large fluctuations in atomic emission, providing new insights into excitation behavior during these events.

## Key findings

- Approximately half of the atoms are excited during large fluctuations.
- The excitation level during large fluctuations is independent of the stationary state.
- Two analytical methods effectively describe the probability and time dependence of fluctuations.

## Abstract

We study the large fluctuations of emitted radiations in the system of $N$ non-interacting two-level atoms. Two methods are used to calculate the probability of the large fluctuations and the time dependence of the excitation and emission. The first method is based on the large deviation principle for Markov processes. The second one uses an analogue of the quantum formalism for classical probability problems. Particularly we prove that in a large fluctuation limit approximately a half of the atoms are excited. This fact is independent on the fraction of the excited atoms in the stationary state.