The Scott conjecture for large Coulomb systems: a review

Abstract

We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe properties of many-particle systems in the limit of a large number of particles. Particular emphasis is put on models that take relativistic kinematics into account. While non-relativistic models are typically rather well understood, this is generally not the case for relativistic ones and leads to a variety of open questions.

62 pages

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Cited by in corpus (5)

• Seven Useful Questions in Density Functional Theory
• On Sobolev norms involving Hardy operators in a half-space
• Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels
• Approximate normalizations for approximate density functionals
• The Ground State Energy of Heavy Atoms: Leading and Subleading Asymptotics