相关论文: On crystal ground state in the Schr\"odinger-Poiss…

A space-periodic ground state is shown to exist for lattices of smeared ions in $\R^3$ coupled to the Schr\"odinger and scalar fields. The elementary cell is necessarily neutral. The 1D, 2D and 3D lattices in $\R^3$ are considered, and a…

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)…

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…

The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the…

We survey our recent results on stability of 3D crystals in the Schr\"odinger-Poisson-Newton model. We establish orbital stability for the ground state in the case of finite crystal and linear stability for infinite crystals under novel…

We study the ground states for the Schr\"odinger equation with a focusing nonlinearity and a point interaction in dimension three. We establish that ground states exist for every value of the mass; moreover they are positive, radially…

We consider the Schr\"odinger--Poisson--Newton equations for crystals with a cubic lattice and one ion per cell. We linearize this dynamics at the ground state and introduce a novel class of the ion charge densities which provide the…

In this letter, we study the ground state of two spherical macroions of identical radius, but asymmetric bare charge ((Q_{A}>Q_{B})). Electroneutrality of the system is insured by the presence of the surrounding divalent counterions. Using…

We consider radial solutions to the Schr\"odinger-Poisson system in three dimensions with an external smooth potential with Coulomb-like decay. Such a system can be viewed as a model for the interaction of dark matter with a bright matter…

We study the ground state structure of electronic-like bilayers, where different phases compete upon changing the inter-layer separation or particle density. New series representations with exceptional convergence properties are derived for…

We consider a spinless, non-relativistic particle bound by an external potential and linearly coupled to a quantized radiation field. The energy $\mathcal{E}(u,f)$ of product states of the form $u\otimes \Psi_f$, where $u$ is a normalized…

We study the existence and the properties of ground states at fixed mass for a focusing nonlinear Schr\"odinger equation in dimension two with a point interaction, an attractive Coulomb potential and a nonlinearity of power type. We prove…

We present a stability result for ground states of a Schr\"odinger-Poisson system in $(2+1)$ dimension, modelling the propagation of a light beam through a liquid crystal with nonlocal nonlinear response. The core of the proof is a…

We consider the Falicov-Kimball model in two dimensions in the neutral case, i.e, the number of mobile electrons is equal to the number of ions. For rational densities between 1/3 and 2/5 we prove that the ground state is periodic if the…

Two dimensional suspensions of spherical colloids subject to periodic external fields exhibit a rich variety of molecular crystalline phases. We study in simulations the ground state configurations of dimeric and trimeric systems, that are…

We establish sufficient conditions for the existence of ground states of the following normalized nonlinear Schr\"odinger--Newton system with a point interaction: \[ \begin{cases} - \Delta_\alpha u = w u + \beta u |u|^{p - 2} &\text{on} ~…

Trapped ions in a periodic potential are a paradigm of a frustrated Wigner crystal. The dynamics is captured by a long-range Frenkel-Kontorova model. The classical ground state can be mapped to the one of an antiferromagnetic spin chain…

We study the existence, the nonexistence, and the shape of the ground states of a Nonlinear Schr\"odinger Equation on a manifold called hybrid plane, that consists of a half-line whose origin is connected to a plane. The nonlinearity is of…

We consider ground states of the $N$ coupled fermionic nonlinear Schr\"{o}dinger systems with the Coulomb potential $V(x)$ in the $L^2$-subcritical case. By studying the associated constraint variational problem, we prove the existence of…

We investigate the ground state of a system of interacting particles in small nonlinear lattices with M > 2 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the…