Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions

László Erdős[1]

  • [1] Georgia Institute of Technology, School of Mathematics, Atlanta GA 30332 (USA)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 6, page 1833-1874
  • ISSN: 0373-0956

Abstract

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We show that the lowest eigenvalue of the magnetic Schrödinger operator on a line bundle over a compact Riemann surface M is bounded by the L 1 -norm of the magnetic field B . This implies a similar bound on the multiplicity of the ground state. An example shows that this degeneracy can indeed be comparable with ∫ M | B | even in case of the trivial bundle.

How to cite

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Erdős, László. "Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions." Annales de l’institut Fourier 52.6 (2002): 1833-1874. <http://eudml.org/doc/116029>.

@article{Erdős2002,
abstract = {We show that the lowest eigenvalue of the magnetic Schrödinger operator on a line bundle over a compact Riemann surface $M$ is bounded by the $L^1$-norm of the magnetic field $B$. This implies a similar bound on the multiplicity of the ground state. An example shows that this degeneracy can indeed be comparable with $\int _M \vert B\vert $ even in case of the trivial bundle.},
affiliation = {Georgia Institute of Technology, School of Mathematics, Atlanta GA 30332 (USA)},
author = {Erdős, László},
journal = {Annales de l’institut Fourier},
keywords = {magnetic laplacian; multiplicity of the ground state; Riemann surface; magnetic Laplacian},
language = {eng},
number = {6},
pages = {1833-1874},
publisher = {Association des Annales de l'Institut Fourier},
title = {Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions},
url = {http://eudml.org/doc/116029},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Erdős, László
TI - Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 6
SP - 1833
EP - 1874
AB - We show that the lowest eigenvalue of the magnetic Schrödinger operator on a line bundle over a compact Riemann surface $M$ is bounded by the $L^1$-norm of the magnetic field $B$. This implies a similar bound on the multiplicity of the ground state. An example shows that this degeneracy can indeed be comparable with $\int _M \vert B\vert $ even in case of the trivial bundle.
LA - eng
KW - magnetic laplacian; multiplicity of the ground state; Riemann surface; magnetic Laplacian
UR - http://eudml.org/doc/116029
ER -

References

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