On the theory of cavities with point-like perturbations. Part I: General theory

TL;DR

This paper develops a theoretical framework for analyzing electromagnetic cavities with point-like antenna perturbations, simplifying the problem and addressing divergences in scattering theory to improve understanding of wavefunction measurements.

Contribution

It introduces a self-consistent approach using a renormalized Green function to model antennas as point-like perturbations, extending beyond previous approximations.

Findings

Overcomes divergence issues in scattering series

Validates assumptions in wavefunction measurement techniques

Enables analysis of degenerated states in cavities

Abstract

The theoretical interpretation of measurements of "wavefunctions" and spectra in electromagnetic cavities excited by antennas is considered. Assuming that the characteristic wavelength of the field inside the cavity is much larger than the radius of the antenna, we describe antennas as "point-like perturbations". This approach strongly simplifies the problem reducing the whole information on the antenna to four effective constants. In the framework of this approach we overcame the divergency of series of the phenomenological scattering theory and justify assumptions lying at the heart of "wavefunction measurements". This selfconsistent approach allowed us to go beyond the one-pole approximation, in particular, to treat the experiments with degenerated states. The central idea of the approach is to introduce ``renormalized'' Green function, which contains the information on boundary reflections and has no singularity inside the cavity.