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res:
bibo_abstract:
- We consider a large neutral molecule with total nuclear charge Z in a model with
self-generated classical magnetic field and where the kinetic energy of the electrons
is treated relativistically. To ensure stability, we assume that Zα < 2/π,
where α denotes the fine structure constant. We are interested in the ground state
energy in the simultaneous limit Z → ∞, α → 0 such that κ = Zα is fixed. The leading
term in the energy asymptotics is independent of κ, it is given by the Thomas-Fermi
energy of order Z7/3 and it is unchanged by including the self-generated magnetic
field. We prove the first correction term to this energy, the so-called Scott
correction of the form S(αZ)Z2. The current paper extends the result of Solovej
et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)] on the Scott correction
for relativistic molecules to include a self-generated magnetic field. Furthermore,
we show that the corresponding Scott correction function S, first identified by
Solovej et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)], is unchanged by
including a magnetic field. We also prove new Lieb-Thirring inequalities for the
relativistic kinetic energy with magnetic fields.@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: 10.1063/1.3697417
bibo_issue: '9'
bibo_volume: 53
dct_date: 2012^xs_gYear
dct_publisher: American Institute of Physics@
dct_title: Relativistic Scott correction in self-generated magnetic fields@
...