Second order semiclassics with self generated magnetic fields László Erdös ; https://orcid.org/0000-0001-5366-9603 Fournais, Søren Solovej, Jan P 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 &gt; 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. Birkhäuser 2012 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/2772 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> info:eu-repo/semantics/altIdentifier/doi/10.1007/s00023-011-0150-z info:eu-repo/semantics/closedAccess