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res:
bibo_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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: László
foaf_name: László Erdös
foaf_surname: Erdös
foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0001-5366-9603
- foaf_Person:
foaf_givenName: Søren
foaf_name: Fournais, Søren
foaf_surname: Fournais
- foaf_Person:
foaf_givenName: Jan
foaf_name: Solovej, Jan P
foaf_surname: Solovej
bibo_doi: 10.1007/s00023-011-0150-z
bibo_issue: '4'
bibo_volume: 13
dct_date: 2012^xs_gYear
dct_publisher: Birkhäuser@
dct_title: Second order semiclassics with self generated magnetic fields@
...