Second order semiclassics with self-generated magnetic fields

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

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 2 and we minimize over all magnetic fields. The parameter ß effectively determines the strength of the field. We consider the weak field regime with ßh2 = 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 (Erdos 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.
OriginalsprogEngelsk
TidsskriftAnnales Henri Poincare
Vol/bind13
Udgave nummer4
Sider (fra-til)671-713
Antal sider43
ISSN1424-0637
DOI
StatusUdgivet - 2012

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