{"citation":{"ista":"Erdös L, Fournais S, Solovej J. 2012. Relativistic Scott correction in self-generated magnetic fields. Journal of Mathematical Physics. 53(9).","chicago":"Erdös, László, Søren Fournais, and Jan Solovej. “Relativistic Scott Correction in Self-Generated Magnetic Fields.” <i>Journal of Mathematical Physics</i>. American Institute of Physics, 2012. <a href=\"https://doi.org/10.1063/1.3697417\">https://doi.org/10.1063/1.3697417</a>.","apa":"Erdös, L., Fournais, S., &#38; Solovej, J. (2012). Relativistic Scott correction in self-generated magnetic fields. <i>Journal of Mathematical Physics</i>. American Institute of Physics. <a href=\"https://doi.org/10.1063/1.3697417\">https://doi.org/10.1063/1.3697417</a>","mla":"Erdös, László, et al. “Relativistic Scott Correction in Self-Generated Magnetic Fields.” <i>Journal of Mathematical Physics</i>, vol. 53, no. 9, American Institute of Physics, 2012, doi:<a href=\"https://doi.org/10.1063/1.3697417\">10.1063/1.3697417</a>.","ama":"Erdös L, Fournais S, Solovej J. Relativistic Scott correction in self-generated magnetic fields. <i>Journal of Mathematical Physics</i>. 2012;53(9). doi:<a href=\"https://doi.org/10.1063/1.3697417\">10.1063/1.3697417</a>","short":"L. Erdös, S. Fournais, J. Solovej, Journal of Mathematical Physics 53 (2012).","ieee":"L. Erdös, S. Fournais, and J. Solovej, “Relativistic Scott correction in self-generated magnetic fields,” <i>Journal of Mathematical Physics</i>, vol. 53, no. 9. American Institute of Physics, 2012."},"month":"09","date_created":"2018-12-11T11:59:32Z","status":"public","publisher":"American Institute of Physics","year":"2012","day":"28","date_published":"2012-09-28T00:00:00Z","date_updated":"2021-01-12T06:59:37Z","publist_id":"4113","volume":53,"extern":1,"type":"journal_article","intvolume":"        53","_id":"2777","doi":"10.1063/1.3697417","author":[{"orcid":"0000-0001-5366-9603","full_name":"László Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"last_name":"Fournais","full_name":"Fournais, Søren","first_name":"Søren"},{"full_name":"Solovej, Jan P","first_name":"Jan","last_name":"Solovej"}],"quality_controlled":0,"title":"Relativistic Scott correction in self-generated magnetic fields","publication":"Journal of Mathematical Physics","publication_status":"published","issue":"9","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 &lt; 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."}]}