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 Type	Single-year Grants
Section	一般
Research Field	Basic analysis
Research Institution	Tokyo 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
Keywords	random 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.

(2 results)