Scattering by magnetic fields and Aharonov-Bohm effect

磁场和阿哈罗诺夫-玻姆效应的散射

• 批准号: 13640176
• 负责人: TAMURA Hideo
• 金额: $ 2.18万
• 依托单位: OKAYAMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640176/
• 关键词: magnetic Scchrodinger operator; Aharonov-Bohm effect; δ-like magnetic field; scattering arnplitude; Aharonov-Bohm effect; scattering by magnetic field; point-like magneticfield; scattreing amplitude; magnetic scattering; scattering amplitude; ma

The present project has been devoted to the study on the scattering problem by several point-like magnetic fields in two dimensions. According to the Aharonov-Bohm effect, magnetic potentials have a direct significance to the motion of particles in quantum mechanics. We study this quantum effect through the scattering by several point-like magnetic fields at large separation in two dimensions. We derive the asymptotic formula for scattering amplitudes as the distances between centers of fields go to infinity. A special emphasis is placed on the case of scattering by fields with centers on an even line. The obtained result depends on fluxes of fields and on ratios of distances between adjacent centers. We figure the approximate values obtained from the asymptotic formula for the differential cross sections and we see how the pattern of interferences changes with flux parameters.

本课题主要研究二维点状磁场的散射问题。根据Aharonov-Bohm效应，磁势在量子力学中对粒子的运动有直接的意义。我们通过几个点状磁场在二维大间距下的散射来研究这种量子效应。我们导出了当场中心之间的距离趋于无穷大时散射振幅的渐近公式。特别强调了中心在一条偶数线上的场的散射情况。得到的结果取决于场的通量和相邻中心之间的距离比。我们计算了微分截面的渐近公式的近似值，并观察了干涉的模式如何随通量参数变化。

项目成果

H. T. Ito and H. Tamura: "Aharanov-Bohm effect in scattering by a chain of point-like magnetic fields"Asymptot. Anal, in press. 2002.

H. T. Ito 和 H. Tamura：“点状磁场链散射中的阿哈拉诺夫-玻姆效应”渐近线。

田村 英男-一瀬 孝: "The norm convergence of the Trotter-Kato product with error bound"Commun.Math.Phys.. 217. 489-502 (2001)

Hideo Tamura-Takashi Ichinose：“具有误差界限的 Trotter-Kato 乘积的范数收敛性”Commun.Math.Phys.. 217. 489-502 (2001)

田村 英男-一瀬 孝, 田村博志-V.A.Zagrebnov: "Note on the paper 1 "The norm convergence of the Trotter-Kato product formula with error bound" by Ichinoce and Tamura"Commun.Math.Phys.. 221. 499-510 (2001)

Hideo Tamura-Takashi Ichinose、Hiroshi Tamura-V.A.Zagrebnov：“Ichinoce 和 Tamura 论文 1“带有误差界的 Trotter-Kato 乘积公式的范数收敛性”的注释”Commun.Math.Phys.. 221. 499-510 (2001)

田村 英男, 一瀬 孝: "On the norm convergence of the self-adjoint Trottre-Kato product formula with error bound, Spectral and inverse spectral theory"Proc. Indian Acad. Sci. Math. Sci.. 112. 99-106 (2002)

Hideo Tamura，Takashi Ichinose：“关于带有误差界的自伴 Trottre-Kato 乘积公式的范数收敛性，谱和逆谱理论”Proc. Indian Acad. 112. 99-106 (2002) ）

一瀬 孝, 田村 英男: "The norm convergence of the Trotter-Kato product formula with error bound"Commun.Math.Phys.. 217. 489-502 (2001)

Takashi Ichinose、Hideo Tamura：“具有误差界的 Trotter-Kato 乘积公式的范数收敛性”Commun.Math.Phys.. 217. 489-502 (2001)