Ground state energy of large atoms in a self-generated magnetic field

Abstract

We consider a large atom with nuclear charge $Z$ described by non-relativistic quantum mechanics with classical or quantized electromagnetic field. We prove that the absolute ground state energy, allowing for minimizing over all possible self-generated electromagnetic fields, is given by the non-magnetic Thomas-Fermi theory to leading order in the simultaneous $Z\to \infty$, $\al\to 0$ limit if $Z\al^2\leq κ$ for some universal $\kappa$, where $\al$ is the fine structure constant.

References in corpus (2)

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• A new coherent states approach to semiclassics which gives Scott's correction

Cited by in corpus (13)

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• Scott correction for large atoms and molecules in a self-generated magnetic field
• The Scott conjecture for large Coulomb systems: a review
• The Ground State Energy of Heavy Atoms: the Leading Correction
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• Statistical Theory of the Atom in Momentum Space
• Local trace asymptotics in the self-generated magnetic field
• Asymptotics of the ground state energy for atoms and molecules in the self-generated magnetic field
• Global trace asymptotics in the self-generated magnetic field in the case of Coulomb-like singularities
• Asymptotics of the ground state energy of heavy molecules in self-generated magnetic field
• Asymptotics of the ground state energy of heavy atoms and molecules in combined magnetic field
• The reduced Hartree-Fock model with self-generated magnetic fields
• Asymptotics of the ground state energy of heavy molecules and related topics. II