Relativistic Scott correction in self-generated magnetic fields.
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Relativistic Scott correction in self-generated magnetic fields. / Erdos, Laszlo; Fournais, Søren; Solovej, Jan Philip.
I: Journal of Mathematical Physics, Bind 53, Nr. 9, 2012, s. 095202 .Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Relativistic Scott correction in self-generated magnetic fields.
AU - Erdos, Laszlo
AU - Fournais, Søren
AU - Solovej, Jan Philip
PY - 2012
Y1 - 2012
N2 - 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 $Z \alpha < 2/\pi$, where $\alpha$ denotes the fine structure constant. We are interested in the ground state energy in the simultaneous limit $Z \rightarrow \infty$, $\alpha \rightarrow 0$ such that $\kappa=Z \alpha$ is fixed. The leading term in the energy asymptotics is independent of $\kappa$, it is given by the Thomas-Fermi energy of order $Z^{7/3}$ 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 $S(\alpha Z) Z^2$. The current paper extends the result of \cite{SSS} 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 in \cite{SSS}, is unchanged by including a magnetic field. We also prove new Lieb-Thirring inequalities for the relativistic kinetic energy with magnetic fields.
AB - 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 $Z \alpha < 2/\pi$, where $\alpha$ denotes the fine structure constant. We are interested in the ground state energy in the simultaneous limit $Z \rightarrow \infty$, $\alpha \rightarrow 0$ such that $\kappa=Z \alpha$ is fixed. The leading term in the energy asymptotics is independent of $\kappa$, it is given by the Thomas-Fermi energy of order $Z^{7/3}$ 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 $S(\alpha Z) Z^2$. The current paper extends the result of \cite{SSS} 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 in \cite{SSS}, is unchanged by including a magnetic field. We also prove new Lieb-Thirring inequalities for the relativistic kinetic energy with magnetic fields.
U2 - 10.1063/1.3697417
DO - 10.1063/1.3697417
M3 - Journal article
VL - 53
SP - 095202
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 9
ER -
ID: 40301930