Metrics for two electron random potential systems

TL;DR

This paper explores the relationship between wavefunction and density distances in two-electron systems with random potentials, demonstrating Fourier series as effective for generating these potentials and revealing quasi-linear relationships relevant to Density Functional Theory.

Contribution

It extends previous work to two-electron systems with random potentials, providing a new framework for exploring density functional theory relationships.

Findings

Fourier series effectively generate random potentials.

Quasi-linear relationships observed between density and wavefunction distances.

Framework supports further exploration of density functional theory.

Abstract

Metrics have been used to investigate the relationship between wavefunction distances and density distances for families of specific systems. We extend this research to look at random potentials for time-dependent single electron systems, and for ground-state two electron systems. We find that Fourier series are a good basis for generating random potentials. These random potentials also yield quasi-linear relationships between the distances of ground-state densities and wavefunctions, providing a framework in which Density Functional Theory can be explored.