Related papers: Electronic Structures of Quantum Dots and the Ulti…
We present an analytically solvable model of $P$ colinear, two-dimensional quantum dots, each containing two electrons. Inter-dot coupling via the electron-electron interaction gives rise to sets of entangled ground states. These ground…
Atomic-like systems in which electronic motion is two dimensional are now realizable as ``quantum dots''. In place of the attraction of a nucleus there is a confining potential, usually assumed to be quadratic. Additionally, a perpendicular…
We study the ground state properties of rectangular quantum dots by using the spin-density-functional theory and quantum Monte Carlo methods. The dot geometry is determined by an infinite hard-wall potential to enable comparison to…
We consider quantum dots with a parabolic confining potential. The qualitative features of such mesoscopic systems as functions of the total number of electrons N and their total angular momentum J, e.g. magic numbers, overall symmetries…
The symmetry constraints imposing on the quantum states of a dot with 13 electrons has been investigated. Based on this study, the favorable structures (FSs) of each state has been identified. Numerical calculations have been performed to…
Two-dimensional systems containing Ne electrons and Nh holes (Ne>Nh) strongly correlated through Coulomb interactions in the presence of a large magnetic field are studied by exact numerical diagonalization. Low lying states are found to…
A new class of analytic and parameter-free, strongly correlated wave functions of simple functional form is derived for few electrons in two-dimensional quantum dots under high magnetic fields. These wave functions are constructed through…
The internal structure of a composite fermion is investigated for a two dimensional parabolic quantum dot containing three electrons. A Yukawa screened Coulomb interaction is assumed, which allows us to discuss the evolution of the…
An analytical solution of the quantum problem of an electron on a spherical segment with angular confinement potential of the form of rectangular impenetrable walls is presented. It is shown that the problem is reduced to finding solution…
One can confine the two-dimensional electron gas in semiconductor heterostructures electrostatically or by etching techniques such that a small electron island is formed. These man-made ``artificial atoms'' provide the experimental…
It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive…
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem and characterize the set of effectively…
We consider spin-polarized electrons in a single Landau level on a torus. The quantum Hall problem is mapped onto a one-dimensional lattice model with lattice constant $2\pi/L_1$, where $L_1$ is a circumference of the torus (in units of the…
We discuss quantum algebraic structures of the systems of electrons or quasiparticles on a sphere of which center a magnetic monople is located on. We verify that the deformation parameter is related to the filling ratio of the particles in…
Infinite families of multi-indexed orthogonal polynomials are discovered as the solutions of exactly solvable one-dimensional quantum mechanical systems. The simplest examples, the one-indexed orthogonal polynomials, are the infinite…
The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons…
We consider systems of two and three electrons in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the electron plane of motion. We show that the energy levels corresponding to states with high angular…
The correlations in the ground state of interacting electrons in a two-dimensional quantum dot in a high magnetic field are known to undergo a qualitative change from liquid-like to crystal-like as the total angular momentum becomes large.…
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…
The physical regions (domains or basins) within the molecular structure are open systems that exchange charge between them and consequently house a fractional number of electrons (net charge). The natural framework describing the quantum…