Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Lifschitz tail in a magnetic field: the nonclassical regime
Download PDF
Download PDF
  • Article
  • Published: November 1998

Lifschitz tail in a magnetic field: the nonclassical regime

  • László Erdős1 

Probability Theory and Related Fields volume 112, pages 321–371 (1998)Cite this article

  • 167 Accesses

  • 26 Citations

  • Metrics details

Abstract.

We obtain the Lifschitz tail, i.e. the exact low energy asymptotics of the integrated density of states (IDS) of the two-dimensional magnetic Schrödinger operator with a uniform magnetic field and random Poissonian impurities. The single site potential is repulsive and it has a finite but nonzero range. We show that the IDS is a continuous function of the energy at the bottom of the spectrum. This result complements the earlier (nonrigorous) calculations by Brézin, Gross and Itzykson which predict that the IDS is discontinuous at the bottom of the spectrum for zero range (Dirac delta) impurities at low density. We also elucidate the reason behind this apparent controversy. Our methods involve magnetic localization techniques (both in space and energy) in addition to a modified version of the “enlargement of obstacles” method developed by A.-S. Sznitman.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA e-mail: erdos@cims.nyu.edu, , , , , , US

    László Erdős

Authors
  1. László Erdős
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 20 July 1997 / Revised version: 20 April 1998

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Erdős, L. Lifschitz tail in a magnetic field: the nonclassical regime. Probab Theory Relat Fields 112, 321–371 (1998). https://doi.org/10.1007/s004400050193

Download citation

  • Issue Date: November 1998

  • DOI: https://doi.org/10.1007/s004400050193

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • Mathematics Subject Classification (1991): 60K40
  • 82B44
  • 82D30
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature