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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.12504 |
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| _version_ | 1866910032383180800 |
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| author | Blas, H. Fleitas, R. P. N. Laeber Barroso, J. Silva |
| author_facet | Blas, H. Fleitas, R. P. N. Laeber Barroso, J. Silva |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12504 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Heun-function analysis of the Dirac spinor spectrum in a sine-Gordon soliton background Blas, H. Fleitas, R. P. N. Laeber Barroso, J. Silva Mathematical Physics Exactly Solvable and Integrable Systems 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. |
| title | Heun-function analysis of the Dirac spinor spectrum in a sine-Gordon soliton background |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2601.12504 |