Related papers: Comment to "Thomson rings in a disk"
We present a complete resolution of the Abraham-Minkowski controversy . This is done by considering several new aspects which invalidate previous discussions. We show that: 1)For polarized matter the center of mass theorem is no longer…
The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on…
Poisson electrodynamics is the low-energy limit of a rank-one noncommutative gauge theory. It admits a closed formulation in terms of a Poisson structure on the space-time manifold and reproduces ordinary classical electrodynamics in the…
We consider the Coulomb gas of $N$ particles on the sphere and show that the logarithmic energy of the configurations approaches the minimal energy up to an error of order $\log N$, with exponentially high probability and on average,…
In this paper we analyze again a transition from the classical to quantum description of bound charged particles, which involves a substantial modification of the structure of their electromagnetic (EM) fields related to the well-known fact…
We proceed further with the study of minimum weak Riesz energy problems for condensers with touching plates, initiated jointly with Bent Fuglede (Potential Anal. 51 (2019), 197--217). Having now added to the analysis constraint and external…
We numerically examine divergences of the total energy in metallic systems of approximate many-body theories using Hartree--Fock as a reference, including perturbative (M\oller-Plesset, MP), coupled cluster (CC) and configuration…
The energy of magnetic vortex core and its equilibrium radius in thin circular cylinder were first presented by N.A. Usov and S.E. Peschany in 1994. Yet, the magnetostatic function, entering the energy expression, is hard to evaluate and…
An energy functional for orbital based $O(N)$ calculations is proposed, which depends on a number of non orthogonal, localized orbitals larger than the number of occupied states in the system, and on a parameter, the electronic chemical…
We calculate the zero temperature electrostatic properties of charged one and two dimensional arrays of rings, in the classical and quantum limits. Each ring is assumed to be an ideal ring of negligible width, with exactly one electron on…
Several commonly observed physical and biological systems are arranged in shapes that closely resemble an honeycomb cluster, that is, a tessellation of the plane by regular hexagons. Although these shapes are not always the direct product…
Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic…
We derive the most general effective low-energy potential to order O(1/m) for slow Dirac fermions with mass m, coupled to gravitational, chameleon and torsion fields in the Einstein-Cartan gravity. The obtained results can be applied to the…
Elements of group I in the Periodic table have valence electrons of s-type and are usually considered as simple metals. Crystal structures of these elements at ambient pressure are close-packed and high-symmetry of bcc and fcc types,…
Coulomb charges confined by a harmonic potential display a rich structure at strong coupling, both classical and quantum. A simple density functional theory is reviewed showing the essential role of correlations in forming shell structure…
We investigate ground state configurations of atomic systems in two dimensions interacting via short range pair potentials. As the number of particles tends to infinity, we show that low-energy configurations converge to a macroscopic…
The classical (i.e. non-quantum) equilibrium statistical mechanics of a Coulomb fluid living on a pseudosphere (an infinite surface of constant negative curvature) is considered. The Coulomb fluid occupies a large disk communicating with a…
We theoretically investigate the possibility for a tetraneutron to exist as a low-energy resonance state. We explore a microscopic model based on the assumption that the tetraneutron can be treated as a compound system where $^3$n+n and…
In this paper, we study a shape optimization problem for the torsional energy associated with a domain contained in an infinite cylinder, under a volume constraint. We prove that a minimizer exists for all fixed volumes and show some of its…
The configurational and melting properties of large two-dimensional clusters of charged classical particles interacting with each other via the Coulomb potential are investigated through the Monte Carlo simulation technique. The particles…