Spectral analysis of Schrodinger operators with singular magnetic fields in three dimensions

• Project/Area Number: 22540189
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyoto Institute of Technology
• Principal Investigator: IWATSUKA Akira 京都工芸繊維大学, 工芸科学研究科, 教授 (40184890)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 関数方程式論 / 関数解析学 / 数理物理 / スペクトル / 散乱理論 / 国際情報交換 / スペクトル論 / シュレディンガー作用素 / アハラノフ・ボーム効果

Research Abstract

We extended our previous results concerning the norm convergence of the Schrodinger operators to some operator with a singular magnetic field supported on a circle when the the thickness of the torus tends to zero, and showed the absolute continuity of the spectrum of the obtained operator with singular magnetic fields and the asymptotic completeness of its scattering operators.

Research Products

• [Journal Article] Upper bound for the Bethe-Sommerfeld threshold and the spectrum of the Poisson random Hamiltonian in two dimensions (2013)
  • Author(s): M. Kaminaga, T. Mine
  • Journal Title: Annales Henri Poincare Volume: 14 No.1
  • Peer Reviewed
• [Journal Article] Landau levels on the hyperbolic plane in the presence of Aharonov-Bohm fields (2012)
  • Author(s): T. Mine, Y. Nomura
  • Journal Title: J. Funct. Anal Volume: 263 No.6
  • Peer Reviewed
• [Journal Article] Aharonov?Bohm effect in resonances of magnetic Schrodinger operators in two dimensions (2012)
  • Author(s): H. Tamura
  • Journal Title: Kyoto J. Math Volume: 52
  • Peer Reviewed
• [Journal Article] Aharonov?Bohm effect in resonances of magnetic Schrodinger operators with potentials with supports at large separation (2011)
  • Author(s): I. Alexandrova, H. Tamura
  • Journal Title: Ann. Henri Poincare Volume: 12
  • Peer Reviewed
• [Journal Article] Relativistic Hamiltonians with dilation analytic potentials diverging at infinity (2011)
  • Author(s): H. T. Ito, O. Yamada
  • Journal Title: Journal of the Mathematical Society of Japan Volume: Vol. 68 (4) Pages: 1-47
  • Peer Reviewed
• [Journal Article] Spectral properties of Schrodinger operators with singular magnetic fields supported by a circle in R3 (2010)
  • Author(s): A.Iwatsuka, T.Mine, S.Shimada
  • Journal Title: 数理解析研究所講究録 Volume: 1696 Pages: 79-93
• [Journal Article] On the nonrelativistic limit of Dirac operators with potentials diverging at infinity
  • Author(s): H. T. Ito, O. Yamada
  • Journal Title: RIMS Kokyuroku Bessatsu
  • Peer Reviewed
• [Presentation] Schrodinger operators with singular magnetic fields supported by a circle in R^3 (2011)
  • Author(s): IWATSUKA, Akira
  • Organizer: The Third St.Petersburg Conference in Spectral Theory
  • Place of Presentation: Euler International Mathematical Institute, St.Petersburg ロシア(招待講演)
  • Year and Date: 2011-07-05