Related papers: Crystallization in the hexagonal lattice for ionic…
We investigate the ground state of a one-dimensional lattice system that hosts two different kinds of excitations (species) which interact with a power-law potential. Interactions are only present between excitations of the same kind and…
We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or equivalently on the set of atomic measures. It consists of…
By means of exact diagonalization we study the low-energy states of seven electrons in the lowest Landau level which are confined by a cylindric external potential modelling the rest of a macroscopic system and thus controlling the filling…
The crystallization of electrons in quasi low-dimensional solids is studied in a model which retains the full three-dimensional nature of the Coulomb interactions. We show that restricting the electron motion to layers (or chains) gives…
DNA-coated colloids are a popular model system for self-assembly through tunable interactions. The DNA-encoded linkages between particles theoretically allow for very high specificity, but generally no directionality or long-range…
The ground state of interacting particles on a disordered one-dimensional host-lattice is studied by a direct numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice…
Outer crusts of neutron stars and interiors of cool white dwarfs consist of bare atomic nuclei, arranged in a crystal lattice and immersed in a Fermi gas of degenerate electrons. We study electrostatic properties of such Coulomb crystals,…
We study the ground-state structures of identical classical point charges with Coulomb interactions, confined between two symmetric parallel charged walls. For the well understood homogeneous dielectric case with no electrostatic images,…
Crystallization of a classical two-dimensional one-component plasma (electrons interacting with the Coulomb repulsion in a uniform neutralizing positive background) is investigated with a molecular dynamics simulation. The positional and…
We investigate ground state configurations for a general finite number $N$ of particles of the Heitmann-Radin sticky disc pair potential model in two dimensions. Exact energy minimizers are shown to exhibit large microscopic fluctuations…
We investigate one-dimensional periodic chains of alternate type of particles interacting through mirror symmetric potentials. The optimality of the equidistant configuration at fixed density -- also called crystallization -- is shown in…
We consider the crystallization problem for a finite one-dimensional collection of identical hard spheres in a periodic energy landscape. This issue arises in connection with the investigation of crystalline states of ionic dimers, as well…
At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density…
Ionic crystals, such as solid electrolytes and complex oxides, are central to modern technologies for energy storage, sensing, actuation, and other functional applications. An important fundamental issue in the atomic and quantum-scale…
Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our…
Unit-vector fields $\nvec$ on a convex polyhedron $P$ subject to tangent boundary conditions provide a simple model of nematic liquid crystals in prototype bistable displays. The equilibrium and metastable configurations correspond to…
We investigate two-dimensional crystallization phenomena, i.e. minimality of a lattice's patch for interaction energies, with pair potentials of type $(x,y)\mapsto V(\|x-y\|)$ where $\|\cdot\|$ is an arbitrary norm on $\mathbb{R}^2$ and…
Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some…
In this paper, we investigate the ground state properties of a mixture of two species of fermionic atoms in one-dimensional optical lattice, as described by the asymmetric Hubbard model. The quantum phase transition from density wave to…
We apply inverse statistical-mechanical methods to find a simple family of optimized isotropic, monotonic pair potentials, under certain constraints, whose ground states for a wide range of pressures is the diamond crystal. These…