10.1063/1.3697417
László Erdös
László
Erdös0000-0001-5366-9603
Fournais, Søren
Søren
Fournais
Solovej, Jan P
Jan
Solovej
Relativistic Scott correction in self-generated magnetic fields
American Institute of Physics
2012
2018-12-11T11:59:32Z
2019-04-26T07:22:20Z
journal_article
https://research-explorer.app.ist.ac.at/record/2777
https://research-explorer.app.ist.ac.at/record/2777.json
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.