08-172 Hideo TAMURA
Semiclassical analysis for spectral shift functions in magnetic scattering by two solenoidal fields (310K, pdf.file) Sep 28, 08
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Abstract. We study the semiclassical asymptotic behavior of the spectral shift function and of its derivative in magnetic scattering by two solenoidal fields in two dimensions under the assumption that the total magnetic flux vanishes. The system has a trajectory oscillating between the centers of two solenoidal fields. The emphasis is placed on analysing how the trapping effect is reflected in the semiclassical asymptotic formula. We also make a brief comment on the case of scattering by a finite number of solenoidal fields and discuss the relation between the Aharonov-Bohm effect from quantum mechanics and the trapping effect from classical mechanics.

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