螺旋位错处带电粒子的磁局域化与谱不对称性
Magnetic localization and spectral asymmetry of a charged particle at a screw dislocation
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中文总结 AI 辅助
本文研究均匀磁场中螺旋位错处带电粒子的运动，推导其量子问题的精确解，揭示螺旋参数与磁场对粒子局域化及谱不对称性的影响。
中文摘要 AI 辅助
我们研究均匀磁场中在螺旋（screw）位错外部运动的带电粒子。尽管该几何结构在局部是欧氏的，但其全局螺旋标识通过组合量\\(\mathcal{J}=\ell-\beta k\\)耦合守恒的轴向与方位角量。消除循环坐标后，径向运动由\\(\mathcal{J}\\)确定的平方反比项及磁场产生的简谐约束项支配。对应的约化量子问题在\\(q\mathcal{B}_0\neq0\\)时可精确求解，产生等间距谱，且存在与取向相关的能量偏移。径向概率密度依赖于\\(\mathcal{J}\\)，对于固定磁场取向，螺旋修正量子数的相反取值具有相同空间分布但能量不同。径向尺度满足\\(\sqrt{\langle r^2\rangle_n}\propto |q\mathcal{B}_0|^{-1/2}\\)，其中磁长度设定局域化尺度。当\\(q\mathcal{B}_0=0\\)时，约束项消失，问题退化为无尺度的平方反比系统。因此，螺旋参数通过守恒轴向与方位角量的全局耦合进入动力学，而磁场提供径向约束，其取向决定谱不对称性。
英文摘要
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 \(\mathcal{J}=\ell-βk\) After eliminating the cyclic coordinates, the radial motion is governed by an inverse-square term determined by $\mathcal{J}$ and a harmonic confining term generated by the magnetic field. The corresponding reduced quantum problem is exactly solvable for $q\mathcal{B}_0\neq0$, yielding an equally spaced spectrum with an orientation-dependent energy shift. The radial probability density depends on $\mathcal{J}$, 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 \(\sqrt{\langle r^2\rangle_n}\propto |q\mathcal{B}_0|^{-1/2}\), with the magnetic length setting the localization scale. At $q\mathcal{B}_0=0$, 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.
发表机构
- Universidade Federal da Paraíba（帕拉伊巴联邦大学）
- Eastern Mediterranean University（东地中海大学）
- California State University, Fresno（弗雷斯诺州立大学）
- University of Hradec Králové（赫拉德茨克拉洛韦大学）
- Erzurum Technical University（埃尔祖鲁姆理工大学）
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