# Thermal Effects on the Stability of Excited Atoms in Cavities

## TL;DR

This paper investigates how temperature and cavity size influence the decay and stability of excited atoms coupled to an environment modeled by harmonic oscillators, revealing size-dependent thermal effects on atomic excited states.

## Contribution

It introduces a detailed analysis of thermal effects on atomic stability within cavities using dressed states, highlighting size-dependent decay behaviors.

## Key findings

- In large cavities, atoms decay as expected at thermal equilibrium.
- In small cavities, atoms remain partially excited, with stability influenced by temperature.
- Decay rates vary significantly with cavity size and temperature.

## Abstract

An atom, coupled linearly to an environment, is considered in a harmonic approximation in thermal equilibrium inside a cavity. The environment is modeled by an infinite set of harmonic oscillators. We employ the notion of dressed states to investigate the time evolution of the atom initially in the first excited level. In a very large cavity (free space) for a long elapsed time, the atom decays and the value of its occupation number is the physically expected one at a given temperature. For a small cavity the excited atom never completely decays and the stability rate depends on temperature.