Related papers: Quantum dots. A survey of rigorous results
The electronic properties of nanoscale quantum dots are reviewed. The similarities and differences between these `artificial atoms' and real atoms are discussed and, in particular, the effect of electron correlations is examined. It is…
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…
A tool for the identification of the shape of quantum dots is developed. By preparing a two-electron quantum dot, the response of the low-lying excited states to a homogeneous magnetic field, i.e. their spin and parity oscillations, is…
Several topics on the implementation of spin qubits in quantum dots are reviewed. We first provide an introduction to the standard model of quantum computing and the basic criteria for its realization. Other alternative formulations such as…
This is a review of the basic theoretical ideas of quantum criticality, and of their connection to numerous experiments on correlated electron compounds. A shortened, modified, and edited version appeared in Physics Today. This arxiv…
The magnetization of quantum dots is discussed in terms of a relatively simple but exactly solvable model Hamiltonian. The model predicts oscillations in spin polarization as a function of dot radius for a fixed electron density. These…
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives…
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…
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.
We review our recent work addressing various theoretical issues in spin-based quantum dot quantum computation and quantum information processing. In particular, we summarize our calculation of electron exchange interaction in two-electron…
This is a review of some of the concepts and results of the effective field theory treatment of quantum general relativity. Included are lessons of low energy quantum gravity, and a discussion of the limits of effective field theory…
The present status of quantum electrodynamics (QED) theory of heavy few-electron ions is reviewed. The theoretical results are compared with available experimental data. A special attention is focused on tests of QED at strong fields and on…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
We study a small spin-degenerate quantum dot with even number of electrons, weakly connected by point contacts to the metallic electrodes, and subject to an external magnetic field. If the Zeeman energy B is equal to the single-particle…
We present a new method for calculating ground state properties of quantum dots in high magnetic fields. It takes into account the equilibrium positions of electrons in a Wigner cluster to minimize the interaction energy in the high field…
We calculate the magnetization of quantum dots deviating from circular symmetry for noninteracting electrons or electrons interacting according to the Hartree approximation. For few electrons the magnetization is found to depend on their…
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…
We consider the motion of electrons confined to a two dimensional plane with an externally applied perpendicular inhomogeneous magnetic field, both with and without a Coulomb potential. We find that as long as the magnetic field is…
The possibility of a novel type of semiconductor quantum dots obtained by spatially modulating the spin-orbit coupling intensity in III-V heterostructures is discussed. Using the effective mass model we predict confined one-electron states…
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…