Reflection and transmission at dimensional boundaries

TL;DR

This paper investigates how electromagnetic and particle waves scatter at boundaries between regions with different sizes of extra dimensions in higher-dimensional spacetimes, analyzing both analytical limits and numerical solutions.

Contribution

It provides a detailed analysis of wave scattering at dimensional boundaries in Kaluza-Klein models, including analytical limits and numerical results for arbitrary wall thickness.

Findings

Reflection and transmission coefficients depend on wave frequency.

Results resemble those of electroweak and other 4d domain walls.

Qualitative agreement with known domain wall scattering phenomena.

Abstract

An inhomogeneous Kaluza-Klein compactification of a higher dimensional spacetime may give rise to an effective 4d spacetime with distinct domains having different sizes of the extra dimensions. The domains are separated by domain walls generated by the extra dimensional scale factor. The scattering of electromagnetic and massive particle waves at such boundaries is examined here for models without warping or branes. We consider the limits corresponding to thin (thick) domain walls, i.e., limits where wavelengths are large (small) in comparison to wall thickness. We also obtain numerical solutions for a wall of arbitrary thickness and extract the reflection and transmission coefficients as functions of frequency. Results are obtained which qualitatively resemble those for electroweak domain walls and other "ordinary" domain walls for 4d theories.