Spectral and scattering theory for many body quantum systems in electromagnetic fields

• Project/Area Number: 23540201
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kobe University
• Principal Investigator: ADACHI TADAYOSHI 神戸大学, 大学院理学研究科, 教授 (30281158)
• Co-Investigator(Kenkyū-buntansha): MAEKAWA Yasunori 東北大学, 大学院理学研究科, 准教授 (70507954)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 多体問題 / スペクトル理論 / 散乱理論 / 漸近完全性 / 電磁場 / 漸近挙動 / 自己相似解 / 波動作用素 / 安定性

Outline of Final Research Achievements

The achievements of our research are as follows: 1. We showed the asymptotic completeness for some quantum systems in time-periodic homogeneous electric and magnetic fields. 2. We improved some results obtained by previous works on a certain problem of the inverse scattering for quantum systems in homogeneous electric fields asymptotically zero in time. 3. We obtained new results on the asymptotic behavior of the solutions to nonlinear evolution equations, especially which possess self-similar solutions.

Research Products

• [Journal Article] On multidimensional inverse scattering in time-dependent electric fields (2013)
  • Author(s): Adachi, T., Fujiwara, Y., Ishida, A
  • Journal Title: Inverse Problems Volume: 29(no. 8, 085012) Issue: 8 Pages: 24-24
  • DOI: 10.1088/0266-5611/29/8/085012
  • Peer Reviewed
• [Journal Article] Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift (2013)
  • Author(s): H. Miura and Y. Maekawa
  • Journal Title: Journal of Functional Analysis Volume: 264 Issue: 10 Pages: 2245-2268
  • DOI: 10.1016/j.jfa.2013.02.011
  • NAID: 120006459704
  • Peer Reviewed
• [Journal Article] Avron-Herbst type formula in crossed constant magnetic and time-dependent electric fields (2012)
  • Author(s): Adachi, T., Kawamoto, M
  • Journal Title: Lett. Math. Phys Volume: 102(no. 1) Issue: 1 Pages: 65-90
  • DOI: 10.1007/s11005-012-0555-8
  • Peer Reviewed
• [Journal Article] On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis (2012)
  • Author(s): Yoshiyuki Kagei
  • Journal Title: J. Differential Equations Volume: 253 Issue: 11 Pages: 2951-2992
  • DOI: 10.1016/j.jde.2012.08.028
  • NAID: 120005039071
  • Peer Reviewed
• [Journal Article] On multidimensional inverse scattering in an external electric field asymptotically zero in time (2011)
  • Author(s): Adachi, T., Kamada, T., Kazuno, M., Toratani, K
  • Journal Title: Inverse Problems Volume: 27(no. 6, 065006) Issue: 6 Pages: 17-17
  • DOI: 10.1088/0266-5611/27/6/065006
  • Peer Reviewed
• [Journal Article] Scattering in an external electric field asymptotically constant in time (2011)
  • Author(s): Adachi, T., Ishida, A
  • Journal Title: J. Math. Phys Volume: 52(no. 6, 062101) Issue: 6 Pages: 15-15
  • DOI: 10.1063/1.3592600
  • Peer Reviewed
• [Journal Article] Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance (2011)
  • Author(s): Yoshiyuki Kagei
  • Journal Title: J.Functional Analysis Volume: 260 Issue: 10 Pages: 3036-3096
  • DOI: 10.1016/j.jfa.2011.02.004
  • NAID: 120005007645
  • Peer Reviewed
• [Journal Article] Spectral properties of the linearization at the Burgers vortex in the high rotation limit (2011)
  • Author(s): Y. Maekawa
  • Journal Title: Journal of Mathematical Fluid Mechanics Volume: 13 Issue: 4 Pages: 515-532
  • DOI: 10.1007/s00021-010-0048-4
  • Peer Reviewed
• [Presentation] ２次元半空間における渦度方程式の数学解析 (2012)
  • Author(s): 前川泰則
  • Organizer: 日本数学会(招待講演)
  • Place of Presentation: 東京理科大学