2002 Fiscal Year Final Research Report Summary
Scattering by magnetic fields and Aharonov-Bohm effect
| Project/Area Number |
13640176
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | OKAYAMA UNIVERSITY |
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Principal Investigator |
TAMURA Hideo Okayama University Science Prof, 理学部, 教授 (30022734)
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| Co-Investigator(Kenkyū-buntansha) |
IWATSUKA Akira Kyoto Institute of Technology Prof, 繊維学部, 教授 (40184890)
HIROKAWA Masao Okayama University Science Assistant Prof, 理学部, 助教授 (70282788)
KATSUDA Atsushi Okayama University Science Assistant Prof, 理学部, 助教授 (60183779)
ITO Hiroshi Okayama University Engineering Assistant Prof, 工学部, 助教授 (90243005)
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| Project Period (FY) |
2001 – 2002
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| Keywords | magnetic Scchrodinger operator / Aharonov-Bohm effect / δ-like magnetic field / scattering arnplitude |
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| Research Abstract |
The present project has been devoted to the study on the scattering problem by several point-like magnetic fields in two dimensions. According to the Aharonov-Bohm effect, magnetic potentials have a direct significance to the motion of particles in quantum mechanics. We study this quantum effect through the scattering by several point-like magnetic fields at large separation in two dimensions. We derive the asymptotic formula for scattering amplitudes as the distances between centers of fields go to infinity. A special emphasis is placed on the case of scattering by fields with centers on an even line. The obtained result depends on fluxes of fields and on ratios of distances between adjacent centers. We figure the approximate values obtained from the asymptotic formula for the differential cross sections and we see how the pattern of interferences changes with flux parameters.
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