| Project/Area Number |
14540212
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Ehime University |
|---|
Principal Investigator |
ITO Hiroshi Ehime University, Faculty of Engineering, Assistant Professor, 工学部, 助教授 (90243005)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SADAMATSU Takashi Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (10025439)
IGARI Katsujyu Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (90025487)
AMANO Kanarme Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (80113512)
TAMURA Hideo Okayama University, Faculty of science, Professor, 理学部, 教授 (30022734)
YAMADA Osanobu Ritsumeikan University, College of science and engineering, Professor, 理工学部, 教授 (70066744)
|
|---|
| Project Period (FY) |
2002 – 2003
|
| Project Status |
Completed (Fiscal Year 2003)
|
| Budget Amount *help |
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2003: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
|
|---|
| Keywords | Aharonov-Bohm effect / Schrodinger operator / Dirac operator / scattering theory / scattering amplitude / magnetic field / 高エネルギー / 数値等角写像 / ベクトルポテンシャル |
|---|
| Research Abstract |
It is known that an electron may be affected by a magnetic field through an associated vector potential even if the electron does not move in the field. This phenomenon is called the Aharonov-Bohm effect and is a typical one in quantum mechanics. Aharonov and Bohm first investigated the phenomenon by calculating the-scattering amplitudes for scattering of Schrodinger equations with a delta-like magnetic field explicitly. In this research Ito and Tamura have studied Schrodinger operators with several delta-like magnetic fields in two dimensions and have obtained the asymptotics of the scattering amplitudes as the distances between the centers of the fields go to infinity. The form of the leading term depends on how the centers of the fields located in initial or scattering directions. The high-energy asymptotics of the scattering amplitudes, for fixed centers, follow from this result immediately. In the case of Dirac operators Tamura has studied the norm resolvent convergence as the delta-like magnetic field is approximated by smooth magnetic fields with small support. Yamada with his co-workers has studied the unique continuation property for Dirac operators with a delta-like magnetic field in two dimensions and has obtained some results on the absence of eigenvalues for Dirac operators in three dimensions. Amano and Ogata have developed the numerical conformal mapping based on the charge simulation method in view of various applications. Igari has obtained some results on the removal of the singularities of solutions for some partial differential equations and Sadmatsu has studied the well-posedness.
|
