42 research outputs found
Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots
We provide a quantitative determination of the crystallization onset for two
electrons in a parabolic two-dimensional confinement. This system is shown to
be well described by a roto-vibrational model, Wigner crystallization occurring
when the rotational motion gets decoupled from the vibrational one. The Wigner
molecule thus formed is characterized by its moment of inertia and by the
corresponding sequence of rotational excited states. The role of a vertical
magnetic field is also considered. Additional support to the analysis is given
by the Hartree-Fock phase diagram for the ground state and by the random-phase
approximation for the moment of inertia and vibron excitations.Comment: 10 pages, 8 figures, replaced by the published versio
Geometry, stochastic calculus and quantum fields in a non-commutative space-time
The algebras of non-relativistic and of classical mechanics are unstable
algebraic structures. Their deformation towards stable structures leads,
respectively, to relativity and to quantum mechanics. Likewise, the combined
relativistic quantum mechanics algebra is also unstable. Its stabilization
requires the non-commutativity of the space-time coordinates and the existence
of a fundamental length constant. The new relativistic quantum mechanics
algebra has important consequences on the geometry of space-time, on quantum
stochastic calculus and on the construction of quantum fields. Some of these
effects are studied in this paper.Comment: 36 pages Latex, 1 eps figur
Probing the Shape of Quantum Dots with Magnetic Fields
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 studied for a large variety of dot shapes. For any geometric
configuration of the confinement we encounter characteristic spin singlet -
triplet crossovers. The magnetization is shown to be a complementary tool for
probing the shape of the dot.Comment: 11 pages, 4 figure
Energy levels and far-infrared spectroscopy for two electrons in a semiconductor nanoring
The effects of electron-electron interaction of a two-electron nanoring on
the energy levels and far-infrared (FIR) spectroscopy have been investigated
based on a model calculation which is performed within the exactly numerical
diagonalization. It is found that the interaction changes the energy spectra
dramatically, and also shows significant influence on the FIR spectroscopy. The
crossings between the lowest spin-singlet and triplet states induced by the
coulomb interaction are clearly revealed. Our results are related to the
experiment recently carried out by A. Lorke et al. [Phys. Rev. Lett. 84, 2223
(2000)].Comment: 17 pages, 6 figures, revised and accepted by Phys. Rev. B (Dec. 15
(Anti-)self-dual homogeneous vacuum gluon field as an origin of confinement and symmetry breaking in QCD
It is shown that an (anti-)self-dual homogeneous vacuum gluon field appears
in a natural way within the problem of calculation of the QCD partition
function in the form of Euclidean functional integral with periodic boundary
conditions. There is no violation of cluster property within this formulation,
nor are parity, color and rotational symmetries broken explicitly. The massless
limit of the product of the quark masses and condensates, , is calculated to all loop orders. This quantity
does not vanish and is proportional to the gluon condensate appearing due to
the nonzero strength of the vacuum gluon field. We conclude that the gluon
condensate can be considered as an order parameter both for confinement and
chiral symmetry breaking.Comment: 16 pages, LaTe
Coulomb correlation effects in semiconductor quantum dots: The role of dimensionality
We study the energy spectra of small three-dimensional (3D) and
two-dimensional (2D) semiconductor quantum dots through different theoretical
approaches (single-site Hubbard and Hartree-Fock hamiltonians); in the smallest
dots we also compare with exact results. We find that purely 2D models often
lead to an inadequate description of the Coulomb interaction existing in
realistic structures, as a consequence of the overestimated carrier
localization. We show that the dimensionality of the dots has a crucial impact
on (i) the accuracy of the predicted addition spectra; (ii) the range of
validity of approximate theoretical schemes. When applied to realistic 3D
geometries, the latter are found to be much more accurate than in the
corresponding 2D cases for a large class of quantum dots; the single-site
Hubbard hamiltonian is shown to provide a very effective and accurate scheme to
describe quantum dot spectra, leading to good agreement with experiments.Comment: LaTeX 2.09, RevTeX, 25 pages, 9 Encapsulated Postscript figures. To
be published in Physical Review
Quantum-dot lithium in zero magnetic field: Electronic properties, thermodynamics, and a liquid-solid transition in the ground state
Energy spectra, electron densities, pair correlation functions and heat
capacity of a quantum-dot lithium in zero external magnetic field (a system of
three interacting two-dimensional electrons in a parabolic confinement
potential) are studied using the exact diagonalization approach. A particular
attention is given to a Fermi-liquid -- Wigner-solid transition in the ground
state of the dot, induced by the intra-dot Coulomb interaction.Comment: 12 pages, incl. 16 figure
Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory
We examine in non-Abelian gauge theory the heavy quark limit in the presence
of the (anti-)self-dual homogeneous background field and see that a confining
potential emerges, consistent with the Wilson criterion, although the potential
is quadratic and not linear in the quark separation. This builds upon the
well-known feature that propagators in such a background field are entire
functions. The way in which deconfinement can occur at finite temperature is
then studied in the static temporal gauge by calculation of the effective
potential at high temperature. Finally we discuss the problems to be surmounted
in setting up the calculation of the effective potential nonperturbatively on
the lattice.Comment: 31 pages, LaTeX, expanded discussion and derivations in Sections 2
and
Hidden symmetries of two-electron quantum dots in a magnetic field
Using a classical and quantum mechanical analysis, we show that the magnetic
field gives rise to dynamical symmetries of a three-dimensional axially
symmetric two-electron quantum dot with a parabolic confinement. These
symmetries manifest themselves as near-degeneracies in the quantum spectrum at
specific values of the magnetic field and are robust at any strength of the
electron-electron interaction.Comment: 6 pages, 3 figures in a gif forma