On stability of ground states for finite crystals in the Schroedinger-Poisson model

TL;DR

This paper analyzes the stability of ground states in finite crystals modeled by Schr"odinger-Poisson equations, establishing conditions for orbital stability and describing the dynamics with moving ions.

Contribution

It introduces a novel stability analysis for finite crystal ground states under periodic boundary conditions, including the effects of moving ions.

Findings

Orbital stability of periodic ground states established.

Global dynamics with moving ions characterized.

Uniform charge densities under Jellium condition.

Abstract

We consider the Schr\"odinger-Poisson-Newton equations for finite crystals under periodic boundary conditions with one ion per cell of a lattice. The electrons are described by one-particle Schr\"odinger equation. Our main results are i) the global dynamics with moving ions; ii) the orbital stability of periodic ground state under a novel Jellium and Wiener-type conditions on the ion charge density. Under the Jellium condition both ionic and electronic charge densities for the ground state are uniform.