# QLunch: August Bjerg

**Speaker:** August Andersen Bjerg from QMATH

**Title:** The Infinite Thomas-Fermi Atoms

**Abstract:** It is a fundamental question to understand the structure of the periodic table of the elements and why the elements within the same group have similar chemical properties. In this talk we will address this question in the limit as the atomic number Z tends towards infinity. Is it possible to understand which elements are similar in this limit and why? We will discuss this in the context of a Thomas-Fermi (TF) mean field model. For each finite nuclear charge Z we describe the atom with the 3-dimensional Schrödinger operator with a mean field potential coming from the TF density functional theory. These Schrödinger operators are naturally self-adjoint, and the question we will discuss is the following: Does this family of self-adjoint operators in any meaningful way give rise to an/some "infinite TF atom(s)" when considering large Z's?

It turns out that actually it does - they appear as limits of the finite atoms along specific sequences of Z's tending towards infinity. We may interpret this as saying that the tails of these sequences represent atoms with similar properties. The infinite atoms are naturally parametrized by the unit circle and in this sense recover a periodicity aspect even for infinite atoms. This all relies on a mathematical result that will be described in detail in the talk where we will also present its generalization to a wider class of potentials having TF-like scaling properties. Based on work in progress with Jan Philip Solovej.