---
_id: '2772'
abstract:
- lang: eng
  text: We consider the semiclassical asymptotics of the sum of negative eigenvalues
    of the three-dimensional Pauli operator with an external potential and a self-generated
    magnetic field B. We also add the field energy β ∫ B 2 and we minimize over all
    magnetic fields. The parameter β effectively determines the strength of the field.
    We consider the weak field regime with βh 2 ≥ const > 0, where h is the semiclassical
    parameter. For smooth potentials we prove that the semiclassical asymptotics of
    the total energy is given by the non-magnetic Weyl term to leading order with
    an error bound that is smaller by a factor h 1+e{open}, i. e. the subleading term
    vanishes. However for potentials with a Coulomb singularity, the subleading term
    does not vanish due to the non-semiclassical effect of the singularity. Combined
    with a multiscale technique, this refined estimate is used in the companion paper
    (Erdo{double acute}s et al. in Scott correction for large molecules with a self-generated
    magnetic field, Preprint, 2011) to prove the second order Scott correction to
    the ground state energy of large atoms and molecules.
author:
- first_name: László
  full_name: László Erdös
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Søren
  full_name: Fournais, Søren
  last_name: Fournais
- first_name: Jan
  full_name: Solovej, Jan P
  last_name: Solovej
citation:
  ama: Erdös L, Fournais S, Solovej J. Second order semiclassics with self generated
    magnetic fields. <i>Annales Henri Poincare</i>. 2012;13(4):671-730. doi:<a href="https://doi.org/10.1007/s00023-011-0150-z">10.1007/s00023-011-0150-z</a>
  apa: Erdös, L., Fournais, S., &#38; Solovej, J. (2012). Second order semiclassics
    with self generated magnetic fields. <i>Annales Henri Poincare</i>. Birkhäuser.
    <a href="https://doi.org/10.1007/s00023-011-0150-z">https://doi.org/10.1007/s00023-011-0150-z</a>
  chicago: Erdös, László, Søren Fournais, and Jan Solovej. “Second Order Semiclassics
    with Self Generated Magnetic Fields.” <i>Annales Henri Poincare</i>. Birkhäuser,
    2012. <a href="https://doi.org/10.1007/s00023-011-0150-z">https://doi.org/10.1007/s00023-011-0150-z</a>.
  ieee: L. Erdös, S. Fournais, and J. Solovej, “Second order semiclassics with self
    generated magnetic fields,” <i>Annales Henri Poincare</i>, vol. 13, no. 4. Birkhäuser,
    pp. 671–730, 2012.
  ista: Erdös L, Fournais S, Solovej J. 2012. Second order semiclassics with self
    generated magnetic fields. Annales Henri Poincare. 13(4), 671–730.
  mla: Erdös, László, et al. “Second Order Semiclassics with Self Generated Magnetic
    Fields.” <i>Annales Henri Poincare</i>, vol. 13, no. 4, Birkhäuser, 2012, pp.
    671–730, doi:<a href="https://doi.org/10.1007/s00023-011-0150-z">10.1007/s00023-011-0150-z</a>.
  short: L. Erdös, S. Fournais, J. Solovej, Annales Henri Poincare 13 (2012) 671–730.
date_created: 2018-12-11T11:59:31Z
date_published: 2012-05-01T00:00:00Z
date_updated: 2021-01-12T06:59:36Z
day: '01'
doi: 10.1007/s00023-011-0150-z
extern: 1
intvolume: '        13'
issue: '4'
month: '05'
page: 671 - 730
publication: Annales Henri Poincare
publication_status: published
publisher: Birkhäuser
publist_id: '4118'
quality_controlled: 0
status: public
title: Second order semiclassics with self generated magnetic fields
type: journal_article
volume: 13
year: '2012'
...