Related papers: Comment to "Thomson rings in a disk"
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
We consider the minimum Riesz $s$-energy problem on the unit disk $\mathbb D:=\{(x_1,\ldots,x_d)\in\mathbb R^d: x_1=0, x_2^2+x_3^2+\ldots+x_d^2\leq 1\}$ in the Euclidean space $\mathbb R^d$, $d\geq 3$, immersed into a smooth rotationally…
The all-order correlation potential method of accurate atomic structure calculations for atoms with one external electron is extended to include one more class of correlation diagrams to all orders. These are the so-called ladder diagrams…
Density functional and quantum Monte Carlo calculations challenge the existence of a unique ground state structure for certain Si clusters. For Si clusters with more than a dozen atoms the lowest ten isomers are close in energy and for some…
We study the critical points of Coulomb energy considered as a function on configuration spaces associated with certain geometric constraints. Two settings of such kind are discussed in some detail. The first setting arises by considering…
Semitopological Vortices (Q-Rings) are identified to be classical soliton configurations whose stability is attributed to both topological and nontopological charges. We discuss some recent work on the simplest possible realization of such…
Outer crusts of neutron stars and interiors of cool white dwarfs consist of bare atomic nuclei, arranged in a crystal lattice and immersed in a Fermi gas of degenerate electrons. We study electrostatic properties of such Coulomb crystals,…
The binding energies of the ground states and several excited states related to single-particle and -hole states in nuclei around ^{16}O are calculated taking charge dependence into account. Effective interactions on the particle basis are…
With the appropriate choice of parameters and sufficient cooling, charged particles in a circular accelerator are believed to undergo a transition to a highly-ordered crystalline state. The simplest possible crystalline configuration is a…
We consider finite discrete systems consisting of two different atomic types and investigate ground-state configurations for configurational energies featuring two-body short-ranged particle interactions. The atomic potentials favor some…
We investigate quantum vortex ring dynamics at scales smaller than the inter-vortex spacing in quantum turbulence. Through geometrical arguments and high resolution numerical simulations we examine the validity of simple estimates of the…
We consider a system of $N\gg 1$ interacting fermionic particles in three dimensions, confined in a periodic box of volume $1$, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper…
Properties of the "electron gas" - in which conduction electrons interact by means of Coulomb forces but ionic potentials are neglected - change dramatically depending on the balance between kinetic energy and Coulomb repulsion. The limits…
We investigate multipartite entanglement in rings of arbitrary spins with antiferromagnetic interactions between nearest neighbors. In particular, we show that the non-degenerate ground state of rings formed by an even number ($N$) of spins…
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…
Understanding fully the dynamics of coupled electron-nuclear spin systems, which are important for the development of long-lived qubits based on solid-state systems, remains a challenge. We show that in a singly charged semiconductor…
We prove the existence of topological rings in (0,2) theories containing non-anomalous left-moving U(1) currents by which they may be twisted. While the twisted models are not topological, their ground operators form a ring under…
The Poisson problem consists in finding an immersed surface $\Sigma\subset\mathbb{R}^m$ minimising Germain's elastic energy (known as Willmore energy in geometry) with prescribed boundary, boundary Gauss map and area which constitutes a…
We derive the $\sigma$-model for granular metals. It is valid for any relation between the temperature, $T$, and the grain mean level spacing. The continuum limit of the $\sigma$-model describes non-perturbative charging effects in…
In this work we present a model for the determination of the interaction energy for triplet and singlet states in atoms with incomplete filled shells. Our model includes the modification of the Coulomb's law by the interaction between the…