MCS-MP Seminar: Heinz Siedentop

Speaker: Heinz Siedentop (LMU)

Title: Proof of the ionization conjecture for generalized Thomas-Fermi-Weizsäcker atoms

Abstract: We will review the status of the ionization conjecture, in particular we will discuss the Thomas-Fermi-Weizsäcker functional, the most elaborate model of atoms for which the excess charge conjecture in the strict sense ($Q\leq1$) has been shown (Benguria and Lieb (1985)) so far.

Benguria, Brezis, and Lieb generalized the Thomas-Fermi-Weizsäcker functional replacing the classical Thomas-Fermi exponent $p=5/3$ of the nonlinearity by a more general positive exponent $p$. We will address $3/2<p<2$ and show a bound uniform in $Z$. Moreover, in the critical case $p=3/2$ there exists a coupling constant $\gamma_c$ where the bound on $Q$ flips from $0$ for $\gamma\geq\gamma_c$ to a linear bound in $Z$ for $\gamma<\gamma_c$.

The talk is based on joint work with Rafael Benguria.