Semiclassical analysis for magnetic scattering by two solenoidal fields

• Autores: Hiroshi T. Ito, Hideo Tamura
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 74, Nº 3, 2006, págs. 695-716
• Idioma: inglés
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• Resumen

  • 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.