相关论文: Ground state of two electrons on concentric sphere…

We have performed a comprehensive study of the singlet ground state of two electrons on the surface of a sphere of radius $R$. We have used electronic structure models ranging from restricted and unrestricted Hartree-Fock theory to…

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…

We show that the exact wave function for two electrons, interacting through a Coulomb potential but constrained to remain on the surface of a $\mathcal{D}$-sphere ($\mathcal{D} \ge 1$), is a polynomial in the interelectronic distance $u$…

The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical…

We investigate the behavior of disordered interacting electrons in the insulating regime. Our study is based on the quantum Coulomb glass model which is obtained from the classical Coulomb glass by adding hopping matrix elements between…

We show that the exact solution of the Schr\"odinger equation for two electrons confined to two distinct concentric rings or spheres can be found in closed form for particular sets of the ring or sphere radii. In the case of two concentric…

Studying the electronic structure of defects in materials is an important subject in condensed matter physics. From a mathematical point of view, nonlinear mean-field models of localized defects in insulators are well understood. We present…

Donor-based quantum devices in silicon are attractive platforms for universal quantum computing and analog quantum simulations. The nearly-atomic precision in dopant placement promises great control over the quantum properties of these…

We analyzed the Hartree-Fock approximation for an electron system. The interaction between particles is modeled by a non-Coulombian potential. We analyzed both the three-dimensional and two-dimensional systems. We obtained accurate…

In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles…

The problem of interacting electrons moving under the influence of a strong magnetic field in two dimensions on a finite disk is reconsidered. First, the results of exact diagonalizations for up to $N=9$ electrons for Coulomb as well as for…

We study the ground state and the collective excitations of parabolically-confined double-layer quantum dot systems in a strong magnetic field. We identify parameter regimes where electrons form maximum density droplet states, quantum-dot…

A Hartree--Fock analysis of the ground-state electronic structure of the finite spherical jellium model is carried out for systems containing up to $520$ electrons in a positive background field with densities ranging from $10^{-3}$ to $1$.…

We explore the existence and behaviour of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with $n$ basis functions is rigorously identified as…

We study the ground-state correlation energy $E_{\rm c}$ of two electrons of opposite spin confined within a $D$-dimensional ball ($D \ge 2$) of radius $R$. In the high-density regime, we report accurate results for the exact and restricted…

An implementation of the Hartree-Fock (HF) method capable of robust convergence for well-behaved arbitrary central potentials is presented. The Hartree-Fock equations are converted to a generalized eigenvalue problem by employing a B-spline…

The GW approximation for the electronic self-energy is an important tool for the quantitative prediction of excited states in solids, but its mathematical exploration is hampered by the fact that it must, in general, be evaluated…

We report on numerical studies into the interplay of disorder and electron-electron interactions within the integer quantum Hall regime, where the presence of a strong magnetic field and two-dimensional confinement of the electronic system…

In this paper, we investigate the ground state of two-dimensional disordered cylinders which contain spinless, interacting electrons using the Hartree-Fock approximation. Calculations of the deviation of the polarization from uniformity…

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…