Relativistic Scott correction for atoms and molecules

Solovej, Jan Philip; Sørensen, Thomas Østergaard; Spitzer, Wolfgang

doi:10.1002/cpa.20296

Cited by 53 publications

(80 citation statements)

References 39 publications

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“…In the special case d = 3 and s = 1/2 this is a recent result by Solovej, Sørensen and Spitzer [SoSøSp,Thm. 11].…”

Section: This Paper Is Concerned With Estimates On Moments Of Negativsupporting

confidence: 70%

A Simple Proof of Hardy-Lieb-Thirring Inequalities

Frank

2009

Commun. Math. Phys.

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Abstract:We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schrödinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Sørensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).

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“…In the special case d = 3 and s = 1/2 this is a recent result by Solovej, Sørensen and Spitzer [SoSøSp,Thm. 11].…”

Section: This Paper Is Concerned With Estimates On Moments Of Negativsupporting

confidence: 70%

A Simple Proof of Hardy-Lieb-Thirring Inequalities

Frank

2009

Commun. Math. Phys.

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“…Constantly adjusting the parameter α in T (α) (A), we can show that the localization errors can be controlled essentially as effectively as in Ref. 21 despite the lack of any explicit formula.…”

Section: (Existence Of Scott Term)mentioning

confidence: 66%

“…21 is not applicable with a magnetic field since it relies on the explicit formula for the relativistic heat kernel. Instead, we use the usual IMS formula under the square root, then apply the operator monotonicity of the square root function and a useful "pull-out" inequality (Lemma 3.1).…”

Section: (Existence Of Scott Term)mentioning

confidence: 99%

Relativistic Scott correction in self-generated magnetic fields

Erdős¹,

Fournais

Solovej

2012

Journal of Mathematical Physics

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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.Comment: Small typos corrected, new references adde

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“…This is the scaling behavior of the Thomas-Fermi model. The same leading term has been established for both the nonrelativistic case and for a model with a relativistic kinetic energy term, and has been extended to higher-order terms (the Scott correction) [3], following earlier work on atoms [4]. Simply put: as Z becomes larger, for finite internuclear distances all diatomics have the same leading term in the energy expression, which has the form of the Thomas-Fermi energy.…”

Section: Introductionmentioning

confidence: 83%

Behavior of the Hartree‐Fock energy at short internuclear distances

Gilka

Solovej

Taylor

2011

Int J of Quantum Chemistry

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There are well-established mathematical relationships for the energy of a diatomic molecule (the exact energy, but also both the Hartree-Fock and Thomas-Fermi energies) in the limit of large nuclear charge of the atoms and small internuclear distances. We present calculated energies for a number of homonuclear diatomic molecules at short internuclear distances for numerical comparison with these established relationships. Intriguingly, they hold in practice for relatively small nuclear charges and for relatively long internuclear distances.

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Relativistic Scott correction for atoms and molecules

Cited by 53 publications

References 39 publications

A Simple Proof of Hardy-Lieb-Thirring Inequalities

A Simple Proof of Hardy-Lieb-Thirring Inequalities

Relativistic Scott correction in self-generated magnetic fields

Behavior of the Hartree‐Fock energy at short internuclear distances

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