@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},
}