Related papers: Symmetric patterns of dislocations in Thomson's pr…
In the present paper we discuss arguments, favouring the view that massive fermions represent dislocations (i.e. topological solitons) in discrete space-time with Burgers vectors, parallel to an axis of time. If to put symmetrical parts of…
Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of 1-form is the local…
Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the…
Finding the ground states of identical particles packed on spheres has relevance for stabilizing emulsions and a venerable history in the literature of theoretical physics and mathematics. Theory and experiment have confirmed that defects…
We attack generalized Thomson problems with a continuum formalism which exploits a universal long range interaction between defects depending on the Young modulus of the underlying lattice. Our predictions for the ground state energy agree…
We have studied the configurations of minimal energy of $N$ charges on a curve on the plane, interacting with a repulsive potential $V_{ij} = 1/r_{ij}^s$, with $s \geq 1$ and $i,j=1,\dots, N$. Among the examples considered are ellipses of…
Given a natural number N, one may ask what configuration of N points on the two-sphere minimizes the discrete generalized Coulomb energy. If one applies a gradient-based numerical optimization to this problem, one encounters many…
We consider static charged fluid spheres with a cosmological constant. We assume a polytropic equation of state, $p \propto \rho^\Gamma$, and a power law charge distribution, $q\propto r^n$. Using this, we convert the generalised…
Correspondences between the Thomson Problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change configurations of $N\le 100$ electrons into…
This research paper investigates the impact of non-metricity and matter source on the geometry of charged spheres in the presence of anisotropic matter configuration. We use a specific model of extended symmetric teleparallel theory to…
In this paper we study the effect of non-trivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on torus. Using the string-net (fixed-point) wave-function, we propose a…
We give a description of numerical Newton algorithm on a constraint manifold using only the ambient coordinates (usually Euclidean coordinates) and the geometry of the constraint manifold. We apply the numerical Newton algorithm on a sphere…
We discuss the basic principles of a self-organization of a finite number of charged particles interacting via the 1/r Coulomb potential in a disk geometry. Our approach is based on the cyclic symmetry and periodicity of the Coulomb…
In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems…
General topological principles how to transfer the planar orders onto a sphere are considered. Formation of extended topological defects (ETDs), which have a reconstructed inner structure surrounded by perfect initial order, is discussed.…
We have performed a detailed exploration of the energy landscape for configurations of points on the sphere, interacting via the logarithmic potential, and corresponding to local minima of the total energy, up to $N = 160$. The growth of…
We study the ground state of two-dimensional classical electron solids under the influence of modulation-doped impurities by using a simulated annealing molecular dynamics method. By changing the setback distance as a parameter, we find…
A fundamental problem in spherical distance geometry aims to recover an $n$-tuple of points on a 2-sphere in $\mathbb{R}^3$, viewed up to oriented isometry, from $O(n)$ input measurements. We solve this problem using algorithms that employ…
"Topological ordered" phases such as gapped quantum spin-liquids and fractional quantum Hall states possess ground state degeneracy on a torus. We show that the topological nature of this degeneracy has interesting consequences for the…
Characterizing the complex spectrum of topological defects in ground states of curved crystals is a long-standing problem with wide implications, from the mathematical Thomson problem to diverse physical realizations, including fullerenes…