Heun-function analysis of the Dirac spinor spectrum in a sine-Gordon soliton background
Abstract
We study the Dirac spectrum in a sine-Gordon soliton background, where the induced position-dependent mass reduces the spectral problem to a Heun-type differential equation. Bound and scattering sectors are treated within a unified framework, with spectral data encoded in Wronskians matching local Heun solutions and exhibiting explicit dependence on the soliton parameters and the bare fermion mass. This formulation enables a systematic analysis of spinor bound and scattering states, supported by analytic and numerical verification of wave function matching across the soliton domain. The present work is related to arXiv:2512.07658 and emphasizes a pedagogical treatment of scattering states within the Heun-equation formalism.
Keywords
Cite
@article{arxiv.2601.12504,
title = {Heun-function analysis of the Dirac spinor spectrum in a sine-Gordon soliton background},
author = {H. Blas and R. P. N. Laeber Fleitas and J. Silva Barroso},
journal= {arXiv preprint arXiv:2601.12504},
year = {2026}
}
Comments
24 pages, 7 figures, Latex. Two appendices added. To be published in the Journal Mato-Grossense de F\'isica