On stability of ground states for finite crystals in the Schrödinger–Poisson model

Abstract

We consider the Schrödinger-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 Schrödinger 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.

On the dispersion decay for crystals in the linearized Schrödinger–Poisson model

“…Recently we have proved the linear stability of these ground states [28]. In [29,30] we have proved the orbital stability of the ground states for the Schrödinger-Poisson equations with one-particle and many-particle Schrödinger equation in the case of finite crystals with periodic boundary conditions.…”

“…The simplest example of such a σ is a constant over the unit cell of a given lattice, which is what physicists usually call Jellium [20]. Moreover, this condition holds for a broad class of functions σ , see [29,Section B.2]. Here we study this model in the rigorous context of the Schrödinger-Poisson equations.…”