Related papers: Exact solution for two interacting electrons on ar…
Evaluating the total energy of an extended distribution of point charges, which interact through the Coulomb potential, is central to the study of condensed matter. With near ubiquity, the summation required is carried out using Ewald's…
We create laterally large and low disorder quantum well based quantum dots to study single electron additions to two dimensional electron systems (2DES). Electrons tunnel into these dots across an AlGaAs tunnel barrier from a single $n+$…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
We present an accurate and efficient algorithm to calculate the electrostatic interaction of charged point particles with partially periodic boundary conditions that are confined along the nonperiodic direction by two metallic parallel…
Exact one-electron eigenstates in finite parts of 1D periodic and Fibonacci chains of attractive and repulsive delta potentials are computed and analyzed. Bloch and bound state boundary conditions are related in terms of transfer matrices.…
Interelectron interactions and correlations in quantum dots can lead to spontaneous symmetry breaking of the self-consistent mean field resulting in formation of Wigner molecules. With the use of spin-and-space unrestricted Hartree-Fock…
We present analytical solutions to a quantum-mechanical three-body problem in three dimensions, which describes a helium-like two-electron atom. Similarly to Hooke's atom, the Coulombic electron-nucleus interaction potentials are replaced…
The exact diagonalization technique is used to study many-particle properties of interacting electrons with spin, confined in a two-dimensional harmonic potential. The single-particle basis is limited to the lowest Landau level. The results…
The magnetic dipole (M1) and electric quadupole (E2) responses of two-dimensional quantum dots with an elliptic shape are theoretically investigated as a function of the dot deformation and applied static magnetic field. Neglecting the…
We present a model for alloys of compound semiconductors by introducing a one-dimensional binary random system where impurities are placed in one sublattice while host atoms lie on the other sublattice. The source of disorder is the…
We provide an algebraic procedure to find the eigenstates of two-charged particles in an oscillator potential, known as {\it{Hooke's}} atom. For the planar Hooke's atom, the exact eigenstates and single particle densities for arbitrary…
The ground states of N-electron parabolic quantum dots in the presence of a perpendicular magnetic field are investigated. Rigorous lower bounds to the ground-state energies are obtained. It is shown that our lower bounds agree well with…
We present a highly flexible computational scheme for studying correlated electrons confined by an arbitrary external potential in two-dimensional semiconductor quantum dots. The method starts by a Lagrange mesh calculation for the…
Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly…
We propose a feasible experimental test of a 1-D version of the Fermi problem using superconducting qubits. We give an explicit non-perturbative proof of strict causality in this model, showing that the probability of excitation of a…
The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are…
The Hubbard on-site repulsion $U$ between opposite spin electrons on the same atomic orbital is widely regarded to be the most important source of electronic correlation in solids. Here we extend the Hubbard model to account for the fact…
We use a simple electrostatic treatment to model recent experiments on quantum Hall systems, in which charging of localised states by addition of integer or fractionally-charged quasiparticles is observed. Treating the localised state as a…
Quantum dots are artificial atoms used for a multitude of purposes. Charge defects are commonly present and can significantly perturb the designed energy spectrum and purpose of the dots. Voltage controlled exchange energy in silicon double…
Using renormalization group techniques, we study spectral and transport properties of a spinless interacting quantum dot consisting of two levels coupled to metallic reservoirs. For strong Coulomb repulsion $U$ and an applied Aharonov-Bohm…