On the response of a system with bound states of particles to the perturbation by the external electromagnetic field

TL;DR

This paper develops a Green function-based framework to analyze how a system of bound fermions, like hydrogen-like atoms, responds to external electromagnetic fields, with applications to plasma and Bose-Einstein condensates.

Contribution

It introduces a method to calculate system response functions considering bound states, enabling analysis of electromagnetic propagation in complex quantum systems.

Findings

Green functions for bound state systems derived

System parameters like conductivity and permittivity expressed in Green functions

Signal propagation with low energy loss in BEC states demonstrated

Abstract

The response of the system, consisting of two kinds of opposite-charged fermions and their bound states (hydrogen-like atoms), to the perturbation by the external electromagnetic field in low particle kinetic energies region is studied. Expressions for Green functions that describe the system response to the external electromagnetic field and take into account the presence of particle bound states (atoms) are found. Macroscopic parameters of the system, such as conductivity, permittivity and magnetic permeability in terms of these Green functions are introduced. As an example, the perturbation of the ideal hydrogen-like plasma by the external electromagnetic field in low temperature region is considered. Such approach also enables to study the propagation properties of the signal, tuned up to the transition between two hyperfine ground state levels of alkali atoms that are considered in Bose-Einstein condensation (BEC) state. It is shown that the signal can propagate in such system with rather small energy loss. Such fact allows to introduce the group velocity concept and to study the slowing down conditions for the microwave signal that propagates in BEC.