---
_id: '2777'
abstract:
- lang: eng
text: 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.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Søren
full_name: Fournais, Søren
last_name: Fournais
- first_name: Jan
full_name: Solovej, Jan P
last_name: Solovej
citation:
ama: Erdös L, Fournais S, Solovej J. Relativistic Scott correction in self-generated
magnetic fields. *Journal of Mathematical Physics*. 2012;53(9). doi:10.1063/1.3697417
apa: Erdös, L., Fournais, S., & Solovej, J. (2012). Relativistic Scott correction
in self-generated magnetic fields. *Journal of Mathematical Physics*. American
Institute of Physics. https://doi.org/10.1063/1.3697417
chicago: Erdös, László, Søren Fournais, and Jan Solovej. “Relativistic Scott Correction
in Self-Generated Magnetic Fields.” *Journal of Mathematical Physics*. American
Institute of Physics, 2012. https://doi.org/10.1063/1.3697417.
ieee: L. Erdös, S. Fournais, and J. Solovej, “Relativistic Scott correction in self-generated
magnetic fields,” *Journal of Mathematical Physics*, vol. 53, no. 9. American
Institute of Physics, 2012.
ista: Erdös L, Fournais S, Solovej J. 2012. Relativistic Scott correction in self-generated
magnetic fields. Journal of Mathematical Physics. 53(9).
mla: Erdös, László, et al. “Relativistic Scott Correction in Self-Generated Magnetic
Fields.” *Journal of Mathematical Physics*, vol. 53, no. 9, American Institute
of Physics, 2012, doi:10.1063/1.3697417.
short: L. Erdös, S. Fournais, J. Solovej, Journal of Mathematical Physics 53 (2012).
date_created: 2018-12-11T11:59:32Z
date_published: 2012-09-28T00:00:00Z
date_updated: 2021-01-12T06:59:37Z
day: '28'
doi: 10.1063/1.3697417
extern: 1
intvolume: ' 53'
issue: '9'
month: '09'
publication: Journal of Mathematical Physics
publication_status: published
publisher: American Institute of Physics
publist_id: '4113'
quality_controlled: 0
status: public
title: Relativistic Scott correction in self-generated magnetic fields
type: journal_article
volume: 53
year: '2012'
...