Relativistic Scott correction in self-generated magnetic fields Journal Article


Author(s): Erdős, László; Fournais, Søren; Solovej, Jan P
Article Title: Relativistic Scott correction in self-generated magnetic fields
Affiliation
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.
Journal Title: Journal of Mathematical Physics
Volume: 53
Issue 9
ISSN: 1089-7658
Publisher: American Institute of Physics  
Date Published: 2012-09-28
Start Page: Article number: 095202
DOI: 10.1063/1.3697417
Open access: no
IST Austria Authors
  1. László Erdős
    110 Erdős
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