---
res:
  bibo_abstract:
  - 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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: László
      foaf_name: László Erdös
      foaf_surname: Erdös
      foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0001-5366-9603
  - foaf_Person:
      foaf_givenName: Søren
      foaf_name: Fournais, Søren
      foaf_surname: Fournais
  - foaf_Person:
      foaf_givenName: Jan
      foaf_name: Solovej, Jan P
      foaf_surname: Solovej
  bibo_doi: 10.1007/s00023-011-0150-z
  bibo_issue: '4'
  bibo_volume: 13
  dct_date: 2012^xs_gYear
  dct_publisher: Birkhäuser@
  dct_title: Second order semiclassics with self generated magnetic fields@
...