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Electrons have three quantized properties -- charge, spin, and Fermi statistics -- that are directly responsible for a vast array of phenomena. Here we show how these properties can be coherently and dynamically stripped from the electron…
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 investigate the dynamics of two interacting electrons confined to a pair of coupled quantum dots driven by an external AC field. By numerically integrating the two-electron Schroedinger equation in time, we find that for certain values…
Manipulating energy levels while controlling the electron localization is an essential step for many applications of confined systems. In this paper we demonstrate how to achieve electron localization and induce energy level oscillation in…
The effects of quantum confinement on the momentum distribution of electrons confined within a cylindrical potential well have been analyzed. The motivation is to understand specific features of the momentum distribution of electrons when…
A two-dimensional array of quantum dots in a magnetic field is considered. The electrons in the quantum dots are described as unitary random matrix ensembles. The strength of the magnetic field is such that there is half a flux quantum per…
A rigorous quantum description of molecular dynamics with a particular emphasis on internal observables is developed accounting explicitly for kinetic couplings between nuclei and electrons. Rotational modes are treated in a genuinely…
An existence theory is established for a coupled non-linear elliptic system, known as "vortex equations", describing the fractional quantum Hall effect in 2-dimensional double-layered electron systems. Via variational methods, we prove the…
The quantum Hall effect is investigated in a high-mobility two-dimensional electron gas on the surface of a cylinder. The novel topology leads to a spatially varying filling factor along the current path. The resulting inhomogeneous…
The full quantum mechanical collapse of a small relativistic dust shell is studied analytically, asymptotically and numerically starting from the exact finite dimensional classical reduced Hamiltonian recently derived by H\'aj{\'\i}\v{c}ek…
We study conductance through a quantum dot under Coulomb blockade conditions in the presence of an external periodic perturbation. The stationary state is determined by the balance between the heating of the dot electrons by the…
A unified approach to decoherence and relaxation of energy resolved single electron excitations in Integer Quantum Hall edge channels is presented. Within the bosonization framework, relaxation and decoherence induced by interactions and…
The Laughlin states for $N$ interacting electrons at the plateaus of the fractional Hall effect are studied in the thermodynamic limit of large $N$. It is shown that this limit leads to the semiclassical regime for these states, thereby…
The role of electronic interactions in the level structure of semiconductor quantum dots is analyzed in terms of the correspondence to the integrability of a classical system that models these structures. We find that an otherwise simple…
We review our investigation of the spin dynamics for two electrons confined to a double quantum dot under the influence of the hyperfine interaction between the electron spins and the surrounding nuclei. Further we propose a scheme to…
The quantum Hall effect occuring in two-dimensional electron gases was first explained by Laughlin, who envisioned a thought experiment that laid the groundwork for our understanding of topological quantum matter. His proposal is based on a…
The internal stability of the electron has been debated for a century at both the classical and the quantum level. Recently, a local force density balance was established for the 1s electron in the H atom, based on the energy-momentum…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
Contrary to common belief, the current emitted by a contact embedded in a two-dimensional electron gas (2DEG) is quantized in the presence of electric and magnetic fields. This observation suggests a simple, clearly defined model for the…
Melting of two dimensional (2D) clusters of classical particles is studied using Brownian dynamics and Langevin molecular dynamics simulations. The particles are confined by a circular hard wall or a parabolic external potential and…