Related papers: Two and three electrons on a sphere: A generalized…
Correspondences between the Thomson Problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change configurations of $N\le 100$ electrons into…
We calculate the spatial entanglement between two electrons trapped in a nanostructure for a broad class of confinement potentials, including single and double quantum dots, and core-shell quantum dot structures. By using a parametrized…
In this perspective, the various measures of electron correlation used in wavefunction theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant…
The energy spectrum of an electron confined to an arbitrary surface of revolution in an external magnetic field, parallel to the symmetry axis, is studied analitycally and numerically. The problem is reduced via conformal mapping to one on…
The intrinsic geometric degree of freedom that was proposed to determine the optimal correlation energy of the fractional quantum Hall states, is analyzed for quantum confined planar electron systems. One major advantage in this case is…
Confined geometries such as semiconductor quantum dots are promising candidates for fabricating quantum computing devices. When several quantum dots are in proximity, spatial correlation between electrons in the system becomes significant.…
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives…
We present a method which computes many-electron energies and eigenfunctions by a full configuration interaction which uses a basis of atomistic tight-binding wave functions. This approach captures electron correlation as well as atomistic…
Solid state physics deals with systems composed of atoms with strongly bound electrons. The tunneling probability of each electron is determined by interactions that typically extend to neighboring sites, as their corresponding wave…
We consider a set of electrostatic problems relevant for determining the real-space structure and the ground-state energy of a two-dimensional electron liquid subject to smooth external potentials. Three fundamental geometries are…
We extend our analysis of two electrons on a sphere [Phys. Rev. A {\bf 79}, 062517 (2009); Phys. Rev. Lett. {\bf 103}, 123008 (2009)] to electrons on concentric spheres with different radii. The strengths and weaknesses of several…
The complex nature of electron-electron correlations is made manifest in the very simple but non-trivial problem of two electrons confined within a sphere. The description of highly non-local correlation and self-interaction effects by…
The properties of a special configuration of a helium-like atomic system, when both electrons are on the surface of a sphere of radius $r$, and angle $\theta$ characterizes their positions on sphere, are investigated. Unlike the previous…
Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it $\Omega$ (the $S^{d-1}-$ sphere, in our…
The energy and wave function of a harmonically confined two-electron system coupled to light is calculated by separating the wave functions of the relative and center of mass (CM) motions. The relative motion wave function has a known…
Entanglement is one of the most fascinating concepts of modern physics. In striking contrast to its abstract, mathematical foundation, its practical side is, however, remarkably underdeveloped. Even for systems of just two orbitals or sites…
This is the second of two papers devoted to tight-binding electronic spectra on graphs with the topology of the sphere. We investigate the problem of an electron subject to a spin-orbit interaction generated by the radial electric field of…
We consider the correlation functions in a gas of electrons moving within a thin layer on the surface of nanosize sphere. A closed form of expressions for the RKKY indirect exchange, superconducting Cooper loop and `density-density'…
Quantum geometry, describing the geometric properties of the Bloch wave function in momentum space, has recently been recognized as a fundamental concept in condensed matter physics. The flat-band system offers the paradigmatic platform…
In this paper, we have given the symmetrical and antisymmetrical spin and space wave functions of three-electron, and further given the full total entanglement states for the three-electron, which are related to their space and spin wave…