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The spectrum of Schrodinger operators with random δ magnetic fields

Authors
Publisher
愛媛大学工学部
Publication Date
Keywords
  • Random Magnetic Field
  • Spectrum
  • Landau Level
  • 500

Abstract

?????????????????????????????????????????????????????????????????????????????????????????? ?????????????????????????? ??????????????????????????????????????????????????? ??????????????????????????????????????? ??????????????? ?????????????????????????????????????????????????????????????????????????????????????? ???????????????????? ??? ????????????????????????????????????????????????????????? ?????? ???? 99 工学ジャーナル 第 7 巻 2008 年 3 月 Annual Journal of Eng., Ehime Univ., VII, Mar., 2008 平成 19 年 8 月 31 日 受付 , 平成 19 年 11 月 7 日 受理 ????? δ ?????????????????? ?????????? The spectrum of Schro¨dinger operators with random δ magnetic fields ?? ??∗ Yuji NOMURA∗ Abstract: We shall consider the Schro¨dinger operators on R2 with the magnetic field given by a non- negative constant field plus random δ magnetic fields of the Anderson type or of the Poisson-Anderson type. We shall investigate the spectrum of these operators by the method of the admissible potentials by Kirsch–Martinelli [23]. Moreover, we shall prove the lower Landau levels are infinitely degenerated eigenvalues when the constant field is sufficiently large, by estimating the growth order of the eigenfunc- tions using the entire function theory by Levin [25]. This article is based on the joint work with Takuya Mine(Kyoto Institute of Technology). Key words: random magnetic field, spectrum, Landau level. 1. ?? δ ??????????? Aharonov–Bohm [1] ????????????Aharonov-Bohm?????? ??Aharonov-Bohm??????????????????????????????? Ruijsenaars [33], Nambu [29], Ito-Tamura [21], ????????????????????? Geyler–Grishanov [19] ??? Geyler–Sˇtˇov´ıcˇek [20] ??????δ ?????? 2?????????? zero-mode?????????? ????????????? [27]?????????????? δ ?????????????? δ ???? ????????????????????????????????? [28]???????? δ ????? ????????????????????????δ ???????????????????????? ????????????????????????????????????????????????? ???????????????? [16, 17, 10, 11, 12]????????? R2 ??????? Lω ? Lω = � 1 i ∇+ aω �2 ????????? ω ????? Ω ???

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