Skip to main content
SpringerLink
Log in

Simplicity of Eigenvalues in the Anderson Model

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We give a transparent and intuitive proof that all eigenvalues of the Anderson model in the region of localization are simple.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Aizenman and S. Molchanov, Localization at large disorder andextreme energies: An elementary derivation, Commun. Math. Phys. 157:245–278 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  2. J. M. Combes and P. D. Hislop, Localization for some continuous, random Hamiltonian in d-dimension, J. Funct. Anal. 124:149–180 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  3. H. von Dreifus and A. Klein, A new proof of localization in the Anderson tight binding model, Commun. Math. Phys. 124:285–299 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Fröhlich, F. Martinelli, E. Scoppola and T. Spencer,Constructive proof of localization in the Anderson tight binding model, Commun. Math. Phys. 101:21–46 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  5. F. Germinet and A. Klein, New characterizations of the region of complete localization for random Schrödinger operators, J. Stat. Phys., to appear.

  6. V. Jaksic and Y. Last, Simplicity of singular spectrum in Anderson type hamiltonians, preprint.

  7. N. Minami, Local fluctuation of the spectrum of a multidimensional Anderson tight binding model, Commun. Math. Phys. 177:709–725 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  8. B. Simon, Cyclic vectors in the Anderson model. Special issue dedicated to Elliott H. Lieb, Rev. Math. Phys. 6:1183–1185 (1994).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Irvine, CA, 92697-3875, USA

    Abel Klein

  2. Department of Mathematics, University of North Carolina at Charlotte, Charlotte, NC, 28223-0001, USA

    Stanislav Molchanov

Authors
  1. Abel Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stanislav Molchanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abel Klein.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Klein, A., Molchanov, S. Simplicity of Eigenvalues in the Anderson Model. J Stat Phys 122, 95–99 (2006). https://doi.org/10.1007/s10955-005-8009-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-005-8009-7

Keywords

Search

Navigation