Magnetic localization and spectral asymmetry of a charged particle at a screw dislocation
Abstract
We study a charged particle moving outside a spiral (screw) dislocation in a uniform magnetic field. Although the geometry is locally Euclidean, its global screw identification couples the conserved axial and azimuthal quantities through the combination 𝒥=ℓ−βk After eliminating the cyclic coordinates, the radial motion is governed by an inverse-square term determined by 𝒥 and a harmonic confining term generated by the magnetic field. The corresponding reduced quantum problem is exactly solvable for qℬ0≠0, yielding an equally spaced spectrum with an orientation-dependent energy shift. The radial probability density depends on 𝒥, and opposite values of the screw-modified quantum number have identical spatial profiles but different energies for a fixed magnetic-field orientation. The radial size scales as √(⟨ r2⟩n)∝ |qℬ0|−1/2, with the magnetic length setting the localization scale. At qℬ0=0, the confining term vanishes, and the problem reduces to a scale-free inverse-square system. Thus, the screw parameter enters the dynamics through the global coupling of the conserved axial and azimuthal quantities, whereas the magnetic field provides radial confinement and its orientation determines the spectral asymmetry.
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BibTeX
@misc{furtado2026magnetic,
title = {{Magnetic localization and spectral asymmetry of a charged particle at a screw dislocation}},
author = {Claudio Furtado and Omar Mustafa and Hassan Hassanabadi and Abdullah Guvendi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10555},
eprint = {2610.10555},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10555},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Magnetic localization and spectral asymmetry of a charged particle at a screw dislocation
AU - Claudio Furtado
AU - Omar Mustafa
AU - Hassan Hassanabadi
AU - Abdullah Guvendi
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.10555
UR - https://arxiv.org/abs/2610.10555
AB - We study a charged particle moving outside a spiral (screw) dislocation in a uniform magnetic field. Although the geometry is locally Euclidean, its global screw identification couples the conserved axial and azimuthal quantities through the combination 𝒥=ℓ−βk After eliminating the cyclic coordinates, the radial motion is governed by an inverse-square term determined by 𝒥 and a harmonic confining term generated by the magnetic field. The corresponding reduced quantum problem is exactly solvable for qℬ_0≠0, yielding an equally spaced spectrum with an orientation-dependent energy shift. The radial probability density depends on 𝒥, and opposite values of the screw-modified quantum number have identical spatial profiles but different energies for a fixed magnetic-field orientation. The radial size scales as √(⟨ r^2⟩_n)∝ |qℬ_0|^−1/2, with the magnetic length setting the localization scale. At qℬ_0=0, the confining term vanishes, and the problem reduces to a scale-free inverse-square system. Thus, the screw parameter enters the dynamics through the global coupling of the conserved axial and azimuthal quantities, whereas the magnetic field provides radial confinement and its orientation determines the spectral asymmetry.
ER -