**
Below is the ascii version of the abstract for 08-172.
The html version should be ready soon.**Hideo TAMURA
Semiclassical analysis for spectral shift functions in magnetic scattering by two solenoidal fields
(310K, pdf.file)
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.