# Relativistic Scott correction in self-generated magnetic fields

Erdös L, Fournais S, Solovej J. 2012. Relativistic Scott correction in self-generated magnetic fields. Journal of Mathematical Physics. 53(9).

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Author

Erdös, László

^{ISTA}^{}; Fournais, Søren; Solovej, Jan PAbstract

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.

Publishing Year

Date Published

2012-09-28

Journal Title

Journal of Mathematical Physics

Volume

53

Issue

9

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### Cite this

Erdös L, Fournais S, Solovej J. Relativistic Scott correction in self-generated magnetic fields.

*Journal of Mathematical Physics*. 2012;53(9). doi:10.1063/1.3697417Erdös, 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/10.1063/1.3697417Erdös, 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.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.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.