@article{2772,
  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.},
  author       = {László Erdös and Fournais, Søren and Solovej, Jan P},
  journal      = {Annales Henri Poincare},
  number       = {4},
  pages        = {671 -- 730},
  publisher    = {Birkhäuser},
  title        = {{Second order semiclassics with self generated magnetic fields}},
  doi          = {10.1007/s00023-011-0150-z},
  volume       = {13},
  year         = {2012},
}