Publication Date:
2011-12-05
Description:
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 b ó õ 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 β h 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 , 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 (Erdős 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. Content Type Journal Article Pages 1-60 DOI 10.1007/s00023-011-0150-z Authors László Erdős, Institute of Mathematics, University of Munich, Theresienstr. 39, 80333 Munich, Germany Søren Fournais, Department of Mathematical Sciences, Aarhus University, Ny Munkegade 118, 8000 Aarhus, Denmark Jan Philip Solovej, Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
Print ISSN:
1424-0637
Electronic ISSN:
1424-0661
Topics:
Mathematics
,
Physics
