Related papers: Two and three electrons on a sphere: A generalized…
We investigate the electronic confinement in bilayer graphene by topological loops of different shapes. These loops are created by lateral gates acting via gap inversion on the two graphene sheets. For large-area loops the spectrum is well…
We consider the problem of correct measurement of a quantum entanglement in the two-body electron-electron scattering. An expression is derived for a spin correlation tensor of a pure two-electron state. A geometrical measure of a quantum…
The ring configurations for classical two-dimensional atoms are calculated within the Thomson model and compared with the results from `exact' numerical simulations. The influence of the functional form of the confinement potential and the…
Some intensive observables of the electronic ground state in condensed matter have a geometrical or even topological nature. In this Review I present the geometrical observables whose expression is known in a full many-body framework,…
The spectra of quantum dots of different geometry (``quantum ring'', ``quantum cylinder'', ``spherical square-well'' and ``parabolic confinement'') are studied. The stochastic variational method on correlated Gaussian basis functions and a…
In this review we first discuss extension of Bohr's 1913 molecular model and show that it corresponds to the large-D limit of a dimensional scaling (D-scaling) analysis, as developed by Herschbach and coworkers. In a separate but synergetic…
With progress towards more compact quantum computing architectures, fundamental questions regarding the entanglement of indistinguishable particles need to be addressed. In a solid state device, this quest is naturally connected to the…
We present a theoretical study of the unielectronic energy spectra, electron localization, and optical absorption of triangular core-shell quantum rings. We show how these properties depend on geometric details of the triangle, such as side…
In this paper, we study several structural models of amorphous silicon, and discuss structural and electronic features common to all. We note spatial correlations between short bonds, and similar correlations between long bonds. Such…
We investigate the scattering of an electron by phonons in a small structure between two one-dimensional tight-binding leads. This model mimics the quantum electron transport through atomic wires or molecular junctions coupled to metallic…
Two entangled electron spins, or qubits, are analyzed in terms of ordinary three-dimensional space geometric properties, as are the angles between their angular momenta. This formulation allows concurrence, a measure of quantum…
Since electrons in a ballistic regime perceive a carbon nanotube or a graphene layer structure as a continuous medium, we can use the study of the quantum dynamics of one electron constrained to a curve or surface to obtain a qualitative…
We present a theory of electronic properties of gated triangular graphene quantum dots with zigzag edges as a function of size and carrier density. We focus on electronic correlations, spin and geometrical effects using a combination of…
We study a system of interacting electrons on a one-dimensional quantum ring using exact diagonalization and the variational quantum Monte Carlo method. We examine the accuracy of the Slater-Jastrow -type many-body wave function and compare…
We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in two-dimensional potentials. We calculate the magnetic susceptibility of singly-connected and the persistent currents of…
The ground state and the excitation spectrum of strongly correlated electrons in quantum dots are investigated. An analytical solution is constructed by exact diagonalization of the Hamiltonian in terms of the $N$-particle eigenmodes.
Calculations for two electrons in an elliptic quantum dot, using symmetry breaking at the unrestricted Hartree-Fock level and subsequent restoration of the broken parity via projection techniques, show that the electrons can localize and…
We propose to quantify the "correlation" inherent in a many-electron (or many-fermion) wavefunction by comparing it to the unique uncorrelated state that has the same single-particle density operator as it does.
Thomson problem is a classical problem in physics to study how $n$ number of charged particles distribute themselves on the surface of a sphere of $k$ dimensions. When $k=2$, i.e. a 2-sphere (a circle), the particles appear at equally…
A Green's function formalism to analyze the scattering properties in confined geometries is developed. This includes scattering from a central field inside the guide created e.g. by impurities. For atomic collisions our approach applies to…