The spectrum of Schrödinger operators with random δ magnetic fields

Takuya Mine[1]; Yuji Nomura[2]

  • [1] Kyoto Institute of Technology Department of Comprehensive Sciences Matsugasaki Sakyo-ku Kyoto 606-8585 (Japan)
  • [2] Ehime University Department of Computer Science Graduate School of Science and Engineering 3 Bunkyo-cho Matsuyama, Ehime 790-8577 (Japan)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 2, page 659-689
  • ISSN: 0373-0956

Abstract

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We shall consider the Schrödinger operators on ℝ 2 with the magnetic field given by a nonnegative 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. 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 eigenfunctions using the entire function theory by Levin.

How to cite

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Mine, Takuya, and Nomura, Yuji. "The spectrum of Schrödinger operators with random $\delta $ magnetic fields." Annales de l’institut Fourier 59.2 (2009): 659-689. <http://eudml.org/doc/10409>.

@article{Mine2009,
abstract = {We shall consider the Schrödinger operators on $\mathbb\{R\}^2$ with the magnetic field given by a nonnegative constant field plus random $\delta $ 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. 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 eigenfunctions using the entire function theory by Levin.},
affiliation = {Kyoto Institute of Technology Department of Comprehensive Sciences Matsugasaki Sakyo-ku Kyoto 606-8585 (Japan); Ehime University Department of Computer Science Graduate School of Science and Engineering 3 Bunkyo-cho Matsuyama, Ehime 790-8577 (Japan)},
author = {Mine, Takuya, Nomura, Yuji},
journal = {Annales de l’institut Fourier},
keywords = {Schrödinger operator; random magnetic field; singular magnetic field; Aharonov-Bohm effect; Landau level; entire function},
language = {eng},
number = {2},
pages = {659-689},
publisher = {Association des Annales de l’institut Fourier},
title = {The spectrum of Schrödinger operators with random $\delta $ magnetic fields},
url = {http://eudml.org/doc/10409},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Mine, Takuya
AU - Nomura, Yuji
TI - The spectrum of Schrödinger operators with random $\delta $ magnetic fields
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 2
SP - 659
EP - 689
AB - We shall consider the Schrödinger operators on $\mathbb{R}^2$ with the magnetic field given by a nonnegative constant field plus random $\delta $ 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. 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 eigenfunctions using the entire function theory by Levin.
LA - eng
KW - Schrödinger operator; random magnetic field; singular magnetic field; Aharonov-Bohm effect; Landau level; entire function
UR - http://eudml.org/doc/10409
ER -

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