Ionization of Atoms in a Thermal Field

TL;DR

This paper investigates the stability of atomic stationary states in a thermal radiation field, showing that states predicted to disintegrate by Fermi's Golden Rule are indeed unstable under small coupling, using spectral analysis of the thermal Hamiltonian.

Contribution

It provides a rigorous spectral analysis demonstrating the instability of certain atomic states in a thermal field, extending understanding of atom-radiation interactions at positive temperature.

Findings

States predicted to disintegrate are unstable when coupled to radiation.

Spectral analysis confirms the instability of these states.

The positive commutator method is effective in this analysis.

Abstract

We study the stationary states of a quantum mechanical system describing an atom coupled to black-body radiation at positive temperature. The stationary states of the non-interacting system are given by product states, where the particle is in a bound state corresponding to an eigenvalue of the particle Hamiltonian, and the field is in its equilibrium state. We show that if Fermi's Golden Rule predicts that a stationary state disintegrates after coupling to the radiation field then it is unstable, provided the coupling constant is sufficiently small (depending on the temperature). The result is proven by analyzing the spectrum of the thermal Hamiltonian (Liouvillian) of the system within the framework of $W^*$-dynamical systems. A key element of our spectral analysis is the positive commutator method.