Related papers: Two electrons on a hypersphere: a quasi-exactly so…
It is shown that the Coulomb correlation problem for a system of two electrons (two charged particles) in an external oscillator potential possesses a hidden $sl_2$-algebraic structure being one of recently-discovered quasi-exactly-solvable…
We investigated resonant multiphoton excitation of high-angular-momentum planetary states of the strontium atom, a quasi-three-body Coulomb system, both experimentally and theoretically. A series of highly doubly excited electronic states…
In this work we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on…
We consider the enhancement of electric field in the presence of two perfectly conducting spheres. When the two spheres get closer, the electric field have a much larger magnitude compared to the external field in the small gap region…
The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of…
We study Haldane's and Jain's proposals for the quasiparticle wave function on the sphere. The expectation values of the energy and the pair angular momenta distribution are calculated at filling factor 1/3 and compared with the data of an…
It is known that homogeneous distribution of particles in Coulomb-like systems can be unstable, and spatially inhomogeneous structures can be formed. A simple method for describing such inhomogeneous systems and obtaining spacial…
We prove that, in the large-dimension limit, the high-density correlation energy $\Ec$ of two opposite-spin electrons confined in a $D$-dimensional space and interacting {\em via} a Coulomb potential is given by $\Ec \sim -1/(8D^2)$ for any…
Structural properties of a finite number ($N = 2 - 20$) of point charges (classical electrons) confined laterally in a two-dimensional two-minima potential are calculated as a function of the distance ($d$) between the minima. The particles…
Continuum states of the Dirac equation are calculated numerically for the electrostatic field generated by the charge distribution of an atomic nucleus. The behavior of the wave functions of an incoming electron with a given asymptotic…
We review some recent progresses in study of the 1D strongly correlated electron systems of long range hopping and exchange. The systems are completely integrable, with infinite number of constants of motions. The results of the physical…
We present exact closed-form expressions and complete asymptotic expansions for the electrostatic force between two charged conducting spheres of arbitrary sizes. Using asymptotic expansions of the force we confirm that even like-charged…
We study Coulomb drag between an active layer with a clean electron liquid and a passive layer with a pinned electron lattice in the regime of fast intralayer equilibration. Such a two-fluid system offers an experimentally realizable way to…
The Einstein - de Broglie particle-soliton concept is applied to simulate stationary states of an electron in a hydrogen atom. According to this concept, the electron is described by the localized regular solutions to some nonlinear…
The electronic distribution functions of two Coulomb coupled chiral edge states forming a quasi-1D system with broken translation invariance are found using the equation of motion approach. We find that relaxation and thereby energy…
We examine the different possible symmetries of the superconducting gap obtained by solving the Eliashberg equations. We consider an electron-phonon interaction in a strong coupling scenario. The Coulomb pseudopotential plays the crucial…
The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane,…
We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
Dipole-dipole interactions which govern phenomena like cooperative Lamb shifts, superradiant decay rates, Van der Waals forces, as well as resonance energy transfer rates are conventionally limited to the Coulombic near-field. Here, we…