---
_id: '2735'
abstract:
- lang: eng
  text: We establish the exact low-energy asymptotics of the integrated density of
    states (Lifschitz tail) in a homogeneous magnetic field and Poissonian impurities
    with a repulsive single-site potential of Gaussian decay. It has been known that
    the Gaussian potential tail discriminates between the so-called “classical” and
    “quantum” regimes, and precise asymptotics are known in these cases. For the borderline
    case, the coexistence of the classical and quantum regimes was conjectured. Here
    we settle this last remaining open case to complete the full picture of the magnetic
    Lifschitz tails.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: 'Erdös L. Lifschitz tail in a magnetic field: Coexistence of classical and
    quantum behavior in the borderline case. <i>Probability Theory and Related Fields</i>.
    2001;121(2):219-236. doi:<a href="https://doi.org/10.1007/PL00008803">10.1007/PL00008803</a>'
  apa: 'Erdös, L. (2001). Lifschitz tail in a magnetic field: Coexistence of classical
    and quantum behavior in the borderline case. <i>Probability Theory and Related
    Fields</i>. Springer. <a href="https://doi.org/10.1007/PL00008803">https://doi.org/10.1007/PL00008803</a>'
  chicago: 'Erdös, László. “Lifschitz Tail in a Magnetic Field: Coexistence of Classical
    and Quantum Behavior in the Borderline Case.” <i>Probability Theory and Related
    Fields</i>. Springer, 2001. <a href="https://doi.org/10.1007/PL00008803">https://doi.org/10.1007/PL00008803</a>.'
  ieee: 'L. Erdös, “Lifschitz tail in a magnetic field: Coexistence of classical and
    quantum behavior in the borderline case,” <i>Probability Theory and Related Fields</i>,
    vol. 121, no. 2. Springer, pp. 219–236, 2001.'
  ista: 'Erdös L. 2001. Lifschitz tail in a magnetic field: Coexistence of classical
    and quantum behavior in the borderline case. Probability Theory and Related Fields.
    121(2), 219–236.'
  mla: 'Erdös, László. “Lifschitz Tail in a Magnetic Field: Coexistence of Classical
    and Quantum Behavior in the Borderline Case.” <i>Probability Theory and Related
    Fields</i>, vol. 121, no. 2, Springer, 2001, pp. 219–36, doi:<a href="https://doi.org/10.1007/PL00008803">10.1007/PL00008803</a>.'
  short: L. Erdös, Probability Theory and Related Fields 121 (2001) 219–236.
date_created: 2018-12-11T11:59:19Z
date_published: 2001-10-01T00:00:00Z
date_updated: 2023-05-16T12:20:42Z
day: '01'
doi: 10.1007/PL00008803
extern: '1'
external_id:
  arxiv:
  - math-ph/0003023
intvolume: '       121'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/math-ph/0003023
month: '10'
oa: 1
oa_version: Published Version
page: 219 - 236
publication: Probability Theory and Related Fields
publication_identifier:
  issn:
  - 0044-3719
publication_status: published
publisher: Springer
publist_id: '4157'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Lifschitz tail in a magnetic field: Coexistence of classical and quantum behavior
  in the borderline case'
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 121
year: '2001'
...
---
_id: '2728'
abstract:
- lang: eng
  text: 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
    &quot;enlargement of obstacles&quot; method developed by A.-S. Sznitman.
acknowledgement: The author is grateful to Professor A.-S. Sznitman for explaining
  him his work and for fruitful discussions, and to the referee for pointing out errors
  and for many helpful comments.This work has been initiated and later on completed
  at the Forschungsinstitut für Mathematik, ETH Zürich.
article_processing_charge: No
article_type: original
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: 'Erdös L. Lifschitz tail in a magnetic field: The nonclassical regime. <i>Probability
    Theory and Related Fields</i>. 1998;112(3):321-371. doi:<a href="https://doi.org/10.1007/s004400050193">10.1007/s004400050193</a>'
  apa: 'Erdös, L. (1998). Lifschitz tail in a magnetic field: The nonclassical regime.
    <i>Probability Theory and Related Fields</i>. Springer. <a href="https://doi.org/10.1007/s004400050193">https://doi.org/10.1007/s004400050193</a>'
  chicago: 'Erdös, László. “Lifschitz Tail in a Magnetic Field: The Nonclassical Regime.”
    <i>Probability Theory and Related Fields</i>. Springer, 1998. <a href="https://doi.org/10.1007/s004400050193">https://doi.org/10.1007/s004400050193</a>.'
  ieee: 'L. Erdös, “Lifschitz tail in a magnetic field: The nonclassical regime,”
    <i>Probability Theory and Related Fields</i>, vol. 112, no. 3. Springer, pp. 321–371,
    1998.'
  ista: 'Erdös L. 1998. Lifschitz tail in a magnetic field: The nonclassical regime.
    Probability Theory and Related Fields. 112(3), 321–371.'
  mla: 'Erdös, László. “Lifschitz Tail in a Magnetic Field: The Nonclassical Regime.”
    <i>Probability Theory and Related Fields</i>, vol. 112, no. 3, Springer, 1998,
    pp. 321–71, doi:<a href="https://doi.org/10.1007/s004400050193">10.1007/s004400050193</a>.'
  short: L. Erdös, Probability Theory and Related Fields 112 (1998) 321–371.
date_created: 2018-12-11T11:59:17Z
date_published: 1998-11-01T00:00:00Z
date_updated: 2022-08-30T08:17:54Z
day: '01'
doi: 10.1007/s004400050193
extern: '1'
intvolume: '       112'
issue: '3'
language:
- iso: eng
month: '11'
oa_version: None
page: 321 - 371
publication: Probability Theory and Related Fields
publication_identifier:
  issn:
  - 0044-3719
publication_status: published
publisher: Springer
publist_id: '4163'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Lifschitz tail in a magnetic field: The nonclassical regime'
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 112
year: '1998'
...