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SEMICLASSICAL ANALYSIS FOR MAGNETIC SCATTERING BY TWO SOLENOIDAL FIELDS

Published online by Cambridge University Press:  04 January 2007

HIROSHI T. ITO  and
HIDEO TAMURA
HIROSHI T. ITO
Affiliation:
Department of Computer Science, Ehime University, Matsuyama 790-8577, Japanito@cs.ehime-u.ac.jp
HIDEO TAMURA
Affiliation:
Department of Mathematics, Okayama University, Okayama 700-8530, Japantamura@math.okayama-u.ac.jp
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Abstract

That vector potentials have a direct significance to quantum particles moving in magnetic fields is known as the A–B (Aharonov–Bohm) effect. We study scattering by two solenoidal magnetic fields (point-like magnetic fields) in two dimensions and analyze the asymptotic behavior of the scattering amplitude in the semiclassical limit. The corresponding classical mechanical system has a trajectory oscillating between the centers of the two fields. We derive the asymptotic formula with the first three terms and make clear how such a trapping trajectory is reflected in the asymptotic formula through the A–B effect. We also make a brief comment on an extension to the scattering by many solenoidal fields. The result depends on the location of the centers of the fields. In particular, the A–B effect appears strongly when the centers are on an even line.

Keywords

81U99 (primary)35P2535Q4081Q70 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 74 , Issue 3 , December 2006 , pp. 695 - 716
Copyright
The London Mathematical Society 2006

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