Related papers: Crystalline Order on a Sphere and the Generalized …
The original Thomson problem of "spherical crystallography" seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of particles interacting with other…
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 complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability…
Topology and geometry of a sphere create constraints for particles that lie on its surface which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately,…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
This paper initiates the systematic study of thermal field theory for generic equilibrium density matrices, which feature arbitrary values not only of temperature and chemical potentials, but also of average angular momentum. The focus here…
The Thomson Problem, arrangement of identical charges on the surface of a sphere, has found many applications in physics, chemistry and biology. Here we show that the energy landscape of the Thomson Problem for $N$ particles with $N=132,…
I review the formalism, Feynman rules, and combinatorics that constrain a field to propagate ``classically", strictly in tree diagrams, either by itself, or interacting with other, purely quantum fields. The perturbation theory is…
Thomson problem is a classical problem in physics to study how $n$ number of charged particles distribute themselves on the surface of a sphere of $k$ dimensions. When $k=2$, i.e. a 2-sphere (a circle), the particles appear at equally…
We investigate the classical ground state of a large number of charges confined inside a disk and interacting via the Coulomb potential. By realizing the important role that the peripheral charges play in determining the lowest energy…
The aim of this paper is to review the classical limit of Quantum Mechanics and to precise the well known threat of chaos (and fundamental graininess)to the correspondence principle. We will introduce a formalism for this classical limit…
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…
Generalizing the classical Thomson problem to the quantum regime provides an ideal model to explore the underlying physics regarding electron correlations. In this work, we systematically investigate the combined effects of the geometry of…
We consider a cosmological scenario endowed with an interaction between the universe's dark components $-$ dark matter and dark energy. Specifically, we assume the dark matter component to be a pressure-less fluid, while the dark energy…
We investigate the impact of the generalized uncertainty principle proposed by some approaches to quantum gravity such as string theory and doubly special relativity on the cosmology. Using generalized Poisson brackets, we obtain the…
We study the (near or close to) ground state distribution of N softly repelling particles trapped in the interior of a spherical box. The charges mutually interact via an inverse power law potential of the form $1/r^\gamma$. We study three…
We propose an additional term in the classical gravitational force law, which is repelling in nature, and which may solve the dark matter problem. As an inverse cube field interaction, it operates over 4 real spatial dimensions and its…
We predict the structural interaction of crystalline solid-melt interfaces using amplitude equations which are derived from classical density functional theory or phase-field-crystal modeling. The solid ordering decays exponentially on the…
The focus of the thesis is to obtain a universal formalism to evaluate the perturbations during inflation at all orders that can be applied to any theory of gravity and matter source in the early universe. We first look at the equivalence…