Mass splitting in the Thomas-Fermi-Dirac-von Weizs\"acker model with background potential

TL;DR

This paper investigates the structure and patterns of minimizers in the Thomas-Fermi-Dirac-von Weizs"acker model when perturbed by a background potential, providing insights into the effects of long-range interactions.

Contribution

It offers a detailed analysis of minimizer sequences and their structure in the TFDW model with background potentials, extending understanding of pattern formation under perturbations.

Findings

Characterization of minimizing sequences in perturbed TFDW models

Description of pattern structures in regularized functionals

Insights into the influence of long-range perturbations on minimizers

Abstract

We consider minimization problems of the Thomas-Fermi-Dirac-von Weizs\"{a}cker (TFDW) type, in which the Newtonian potential is perturbed by a background potential satisfying mild conditions and which ensures the existence of minimizers. We describe the structure of minimizing sequences for those variants, and obtain a more precise characterization of patterns in minimizing sequences for the TFDW functionals regularized by long-range perturbations.