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arXiv 2602.05229quant-ph
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量子螺旋扭曲几何中的散射:类库仑相互作用与Aharonov-Bohm效应

Quantum scattering in helically twisted geometries: Coulomb-like interaction and Aharonov-Bohm effect

Universidade Federal do Maranhão(马拉尼昂联邦大学)

Augusto Tadeu P. de Araújo, Edilberto O. Silva

AI总结:

研究量子粒子在螺旋扭曲几何中散射,揭示类库仑相互作用与Aharonov-Bohm效应的关联,推导散射振幅与截面。

摘要:

我们研究了一个带电量子粒子在螺旋扭曲背景中发生散射的情况,该背景诱导出有效的类库仑相互作用,并存在Aharonov-Bohm(AB)磁通量。从非相对论性薛定谔方程出发,在扭曲度量中推导径向方程,并展示在包含AB势后,其可映射到支配平面2D库仑+AB问题的相同Kummer型微分方程,其中几何诱导的库仑强度和方位量子数被修正为m→m−λ。我们构建了精确的散射解,获得了部分波S矩阵和相移的闭合表达式,并推导了相应的散射振幅、微分散射截面和总散射截面。我们还表明S矩阵的极点结构与之前为螺旋扭曲类库仑问题获得的束缚态量子化一致。

英文摘要:

We investigate the scattering of a charged quantum particle in a helically twisted background that induces an effective Coulomb-like interaction, in the presence of an Aharonov-Bohm (AB) flux. Starting from the nonrelativistic Schrödinger equation in the twisted metric, we derive the radial equation and show that, after including the AB potential, it can be mapped onto the same Kummer-type differential equation that governs the planar $2D$ Coulomb $+$ AB problem, with a geometry-induced Coulomb strength and the azimuthal quantum number shifted as $m\to m-λ$. We construct the exact scattering solutions, obtain closed expressions for the partial-wave $S$ matrix and phase shifts, and derive the corresponding scattering amplitude, differential cross section, and total cross section. We also show that the pole structure of the $S$ matrix is consistent with the bound-state quantization previously obtained for the helically twisted Coulomb-like problem.

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