このエントリーをはてなブックマークに追加
ID 53917
フルテキストURL
著者
Tamura, Hideo Department of Mathematics, Okayama University
抄録
We study the Aharonov–Bohm effect (AB effect) in quantum resonances for magnetic scattering in two dimensions. The system consists of four scatters, two obstacles and two scalar potentials with compact support, which are largely separated from one another. The obstacles by which the magnetic fields are completely shielded are horizontally placed between the supports of the two potentials. The fields do 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 obstacle. This quantum phenomenon is called the AB effect. The resonances are shown to be generated near the real axis by the trajectories trapped between two supports of the scalar potentials as the distances between the scatterers go to infinity. We analyze how the AB effect influences the location of resonances. The result is described in terms of the backward amplitudes for scattering by each of the scalar potentials, and it depends heavily on the ratios of the distances between the four scatterers as well as on the magnetic fluxes of the fields.
キーワード
Aharonov–Bohm effect
magnetic Schrödinger operator
resonances
発行日
2016-01
出版物タイトル
Mathematical Journal of Okayama University
58巻
1号
出版者
Department of Mathematics, Faculty of Science, Okayama University
開始ページ
41
終了ページ
78
ISSN
0030-1566
NCID
AA00723502
資料タイプ
学術雑誌論文
言語
English
著作権者
Copyright©2016 by the Editorial Board of Mathematical Journal of Okayama University
論文のバージョン
publisher
査読
有り
Submission Path
mjou/vol58/iss1/2
JaLCDOI