Aharonov-Bohm effect in resonances for magnetic scattering

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400166
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Okayama University
• Principal Investigator: TAMURA Hideo 岡山大学, 自然科学研究科, 名誉教授 (30022734)
• Co-Investigator(Kenkyū-buntansha): KAKEHI Tomoyuki 岡山大学, 自然科学研究科, 教授 (70231248) ; IWATSUKA Akira 京都工芸繊維大学, 基盤科学系, 教授 (40184890) ; ICHINOSE Takashi 金沢大学, 名誉教授 (20024044)
• Co-Investigator(Renkei-kenkyūsha): MINE Takuya 京都工芸繊維大学, 基盤科学系, 准教授 (90378597) ; FUJIIE Seturo 立命館大学, 理工学部, 教授 (00238536) ; YAJIMA Kenji 学習院大学, 理学部, 教授 (80011758) ; NAKAMURA Shu 東京大学, 数理科学研究科, 教授 (50183520)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: スペクトル理論 / 散乱理論 / シュレディンガー作用素 / 磁場散乱 / アハラノフ・ボーム効果 / レゾナンス / スペクトル漸近解析

Outline of Final Research Achievements

We have studied the Aharonov--Bohm quantum effect in resonances through a simple scattering system in two dimensions. The scattering system consists of four scatterers, two obstacles and two scalar potentials with compact supports, where the obstacles are placed between two supports and shield completely the support of magnetic fields. The field does not influence particles from a classical mechanical point of view, but quantum particles are influenced by the corresponding vector potential which does not necessarily vanish outside the obstacles. We have shown that the resonances are generated near the real axis by the trapping phenomenon between the scatterers and that the location depends on the location of the obstacles as well as on the magnetic fluxes.

Free Research Field

数学解析