Related papers: The Periodic Table in Flatland
In this paper, we investigate periodic vibrations of a group of particles with a dihedral configuration in the plane governed by the Lennard-Jones and Coulomb forces. Using the gradient equivariant degree, we provide a full topological…
In the quantum Hall effect, the density operators at different wave-vectors generally do not commute and give rise to the Girvin MacDonald Plazmann (GMP) algebra with important consequences such as ground-state center of mass degeneracy at…
We investigate the morphology of diblock copolymers in the vicinity of flat, chemically patterned surfaces. Using a Ginzburg-Landau free energy, spatial variations of the order parameter are given in terms of a general two-dimensional…
We construct a new version of the worldline SU(2|1) superspace as a deformation of the standard N =4, d=1 superspace and show that it naturally provides off- and on-shell description of general supersymmetric K\"ahler oscillator model…
The ordering of N equally charged particles (-e) moving in two dimensions and confined by a Coulomb potential, resulting from a displaced positive charge Ze is discussed. This is a classical model system for atoms. We obtain the…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
We study $Q$-ball type solitons in arbitrary spatial dimensions in the setting recently described by Kusenko, where the scalar field potential has a flat direction which rises much slower than $\phi^2$. We find that the general formula for…
The paper presents tetrahedron periodic table to conveniently include superheavy elements. Madelung rule violation statistics is discussed and a model for Madelung rule violation probability calculation is proposed. On its basis superheavy…
I present a new "Pairs of Squares" rendering of the Periodic Table. It takes advantage of the number of orbitals at each Madelung energy level being a whole square. This makes the table very uniform and intuitive in contrast with its…
The fundamental organizing principle resulting in the periodic table is the nuclear charge. Arranging the chemical elements in an increasing atomic number order, a symmetry pattern known as the Periodic Table is detectable. The correlation…
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds…
A Poisson coalgebra analogue of a (non-standard) quantum deformation of sl(2) is shown to generate an integrable geodesic dynamics on certain 2D spaces of non-constant curvature. Such a curvature depends on the quantum deformation parameter…
We consider a physical model where the total energy is governed by surface tension and attractive screened Coulomb potential on the 3-dimensional space. We obtain different periodic equilibrium patterns i.e. stationary sets for this energy,…
The Madelung transformation of the space in which a quantum wave function takes its values is generalized from complex numbers to include field spaces that contain orbits of groups that are diffeomorphic to spheres. The general form for the…
We discuss the variety of coordinates often used to characterize the coherent state classical limit of an algebraic model. We show selection of appropriate coordinates naturally motivates a procedure to generate a single particle…
Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed…
The self-assembly of submonolayer amounts of Au on the densely stepped Si(553) surface creates an array of closely spaced \atomic wires" separated by 1.5 nm. At low temperature, charge transfer between the terraces and the row of silicon…
The $D$-dimensional Smorodinsky-Winternitz system, proposed some years ago by Evans, is re-examined from an algebraic viewpoint. It is shown to possess a potential algebra, as well as a dynamical potential one, in addition to its known…
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum…
We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives…