• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2006 Fiscal Year Final Research Report Summary

Research on spectrum of random magnetic Schr {"o} dinger operators

Research Project

Project/Area Number 17540148
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionTokyo Institute of Technology

Principal Investigator

NOMURA Yuji  Tokyo Institute of Technology, Graduate school of science and engineering, Assistant Professor, 大学院理工学研究科, 助手 (40282818)

Project Period (FY) 2005 – 2006
Keywordsrandom magnetic field / Schr"odinger operator / spectrum
Research Abstract

We consider the magnetic Schr"odinger operator on $mathbf{R}^2$. The magnetic field is the sum of a homogeneous magnetic field and periodically varying pointlike magnetic fields on a lattice. We shall give a sufficient condition for each Landau level to be an infinitely degenerated eigenvalue. This condition is also necessary for the lowest Landau level. In the threshold case, we see that the spectrum near the lowest Landau level is purely absolutely continuous. Moreover, we shall give an estimate for the density of states for Landau levels and their gaps. The proof is based on the method of Geyler and v Sv tov'iv cek, the magnetic Bloch theory, and canonical commutation relations.

  • Research Products

    (2 results)

All 2006

All Journal Article (2 results)

  • [Journal Article] Periodic Aharonov-Bohm Solenoids in a constant magnetic field2006

    • Author(s)
      Mine Takuya, Yuji Nomura
    • Journal Title

      Reviews in mathematical physics Vol. 18, 8

      Pages: 913-934

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Periodic Aharonov-Bohm Solenoids in a constant magnetic field2006

    • Author(s)
      Takuya Mine, Yuji Nomura
    • Journal Title

      Reviews in mathematical physics Vol.18, 8

      Pages: 913-934

    • Description
      「研究成果報告書概要(欧文)」より

URL: 

Published: 2008-05-27  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi