Related papers: Crystallization in the hexagonal lattice for ionic…
We simulate a finite system of $N$ confined electrons with inclusion of the Darwin magnetic interaction in two- and three-dimensions. The lowest energy states are located using the steepest descent quenching adapted for velocity dependent…
We investigate theoretically the ground-state configurations of two-dimensional charged-particle systems with an elliptical hard-wall boundary and their vibrational eigenmodes. The systems exhibit a series of structural transitions, finally…
We study the ground states of cold atoms in the tight-binding bands built from p-orbitals on a two dimensional honeycomb optical lattice. The band structure includes two completely flat bands. Exact many-body ground states with on-site…
It has been shown that to calculate the parameters of the electrostatic field of the ion crystal lattice it sufficient to take into account ions located at a distance of 1-2 lattice spacings. More distant ions make insignificant…
Using the Hartree-Fock approximation, we calculate the energy of different Wigner crystal states for the two-dimensional electron gas of a double quantum well system in a strong magnetic field. Our calculation takes interlayer hopping as…
Mixtures of bare atomic nuclei on a nearly uniform degenerate electron background are a realistic model of matter in the interior of white dwarfs. Despite tremendous progress in understanding their phase diagrams achieved mainly via…
We address finite crystallization in two dimensions in the presence of a flat crystalline substrate. Particles interact through short-range two- and three-body potentials favoring local square-lattice arrangements. An additional interaction…
We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Gamma-convergence. We also…
In this paper we complete the study of global minimizers of a forced, non autonomous, one dimensional, phase transition model, initiated in [8]. Motivated by the recent findings in [9], revealing new configurations of topological structures…
We study the ground-state properties of a system of identical classical Coulombic point particles, evenly distributed between two equivalently charged parallel plates at distance $d$; the system as a whole is electroneutral. It was…
Among lattice configurations of densely packed hard ellipses, Monte Carlo simulations are used to identify the so-called parallel and diagonal lattices as the two favourable states. The free energies of these two states are computed for…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
To our best knowledge there is only one example of a lattice system with long-range two-body interactions whose ground states have been determined exactly: the one-dimensional lattice gas with purely repulsive and strictly convex…
We study the exchange coupling in small Wigner crystals confined to one-dimensional space. In particular we concentrate on the simplest nontrivial case of two electrons in a box potential and calculate analytically the energy splitting…
We study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the…
A two-dimensional atomic mass spring system is investigated for critical fracture loads and its crack path geometry. We rigorously prove that, in the discrete-to-continuum limit, the minimal energy of a crystal under uniaxial tension leads…
We derive exact results for close-packed dimers on the triangular kagome lattice (TKL), formed by inserting triangles into the triangles of the kagome lattice. Because the TKL is a non-bipartite lattice, dimer-dimer correlations are…
It is known that a gas of electrons in a uniform neutralizing background can crystallize and form a lattice if the electron density is less than a critical value. This crystallization may have two- or three-dimensional structure. Since the…
Crystal lattice structure is present in stellar compact objects, such as white dwarf stars and in the crust of neutron stars. These structures can be described by a body-centered cubic crystal, which is formed by ions due to Coulombian…
Whereas many different models exist in the mathematical and physics literature for ground states of non-relativistic crystals, the relativistic case has been much less studied and we are not aware of any mathematical result on a fully…