On orbital stability of ground states for finite crystals in fermionic Schr\"odinger--Poisson model

TL;DR

This paper investigates the stability of ground states in a finite crystal model using the Schrödinger--Poisson equations, establishing conditions for orbital stability and analyzing the dynamics with moving ions.

Contribution

It introduces a novel stability analysis for periodic ground states in a fermionic Schrödinger--Poisson model with moving ions and specific charge density conditions.

Findings

Orbital stability of ground states under Jellium and Wiener-type conditions.

Global dynamics with moving ions established.

Uniform charge densities in ground states under certain conditions.

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 electron field is described by the $N$-particle Schr\"odinger equation with antisymmetric wave function. Our main results are i) the global dynamics with moving ions, and ii) the orbital stability of periodic ground state under a novel Jellium and Wiener-type conditions on the ion charge density. Under Jellium condition both ionic and electronic charge densities of the ground state are uniform.