Related papers: Comment to "Thomson rings in a disk"
We investigate a system of equally charged Coulomb-interacting particles confined to a toroidal helix in the presence of an external electric field. Due to the confinement, the particles experience an effective interaction that oscillates…
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…
The distribution of noncollinear magnetism in an electronic system provides information about the kinetic energy as well as some kinetic energy densities. Two different everywhere-positive kinetic densities related to the…
We present an extension of the spin-adapted configuration-interaction method for the computation of four electrons in a quasi two-dimensional quantum dot. By a group-theoretical decomposition of the basis set and working with relative and…
The purpose of this Letter is to present a computation of the interaction energy of gauged O(3) Chern-Simons vortices which are infinitely separated. The results will show the behaviour of the interaction energy as a function of the…
We report intermolecular potential-energy calculations for solid C_${70}$ and determine the optimum static orientations of the molecules at low temperature; we find them to be consistent with the monoclinic structural model proposed by us…
We study the minimum total weight of a disk triangulation using vertices out of $\{1,\ldots,n\}$, where the boundary is the triangle $(123)$ and the $\binom{n}3$ triangles have independent weights, e.g. $\mathrm{Exp}(1)$ or…
We consider a motion of a weakly relativistic charged particle with an arbitrary spin in central potential $e/r$ in terms of classical mechanics. We show that the spin-orbital interaction causes the precession of the plane of orbit around…
We investigate the ground-state energy and spin of disordered quantum dots using spin-density-functional theory. Fluctuations of addition energies (Coulomb-blockade peak spacings) do not scale with average addition energy but remain…
We investigate the critical points of Coulomb potential of point charges placed at the vertices of a planar polygonal linkage. It is shown that, for a collection of positive charges on a pentagonal linkage, there is a unique critical point…
We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from…
We have attempted to find the global minima of clusters containing between 20 and 80 atoms bound by the Morse potential as a function of the range of the interatomic force. The effect of decreasing the range is to destabilize strained…
In this paper, we consider the Frenkel-Kontorova model of a one dimensional chain of atoms submitted to a potential. This potential splits into an interaction potential and a potential induced by an underlying substrate which is a…
The binding energy of A3C60, a conductor, is described well by an ionic solid type calculation. This succeeds because there is little overlap between molecular wave functions on neighbouring sites, so that electrons are practically…
We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction $\phi_J$. For configurations with a fixed isotropic global stress tensor, we compute the…
We analyzed the localized charge dynamics in the system of $N$ interacting single-level quantum dots (QDs) coupled to the continuous spectrum states in the presence of Coulomb interaction between electrons within the dots. Different dots…
The paper deals with minimum energy problems in the presence of external fields on a locally compact space $X$ with respect to a function kernel $\kappa$ satisfying the energy and consistency principles. For quite a general (not necessarily…
We consider a natural Hamiltonian system with two degrees of freedom and Hamiltonian $H=\|p\|^2/2+V(q)$. The configuration space $M$ is a closed surface (for noncompact $M$ certain conditions at infinity are required). It is well known that…
We consider a non-local interaction energy over bounded densities of fixed mass $m$. We prove that under certain regularity assumptions on the interaction kernel these energies admit minimizers given by characteristic functions of sets when…
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not…