108 research outputs found
Two-Electron Quantum Dot in Magnetic Field: Analytical Results
Two interacting electrons in a harmonic oscillator potential under the
influence of a perpendicular homogeneous magnetic field are considered.
Analytic expressions are obtained for the energy spectrum of the two- and
three-dimensional cases. Exact conditions for phase transitions due to the
electron-electron interaction in a quantum dot as a function of the dot size
and magnetic field are calculated.Comment: 22 pages (Latex file), 3 Postscript figures, to be published in Phys.
Rev.B 55, N 20 (1997
Ground State Spin Oscillations of a Two-Electron Quantum Dot in a Magnetic Field
Crossings between spin-singlet and spin-triplet lowest states are analyzed
within the model of a two-electron quantum dot in a perpendicular magnetic
field. The explicit expressions in terms of the magnetic field, the magnetic
quantum number of the state and the dimensionless dot size for these
crossings are found.Comment: 8 pages, 2 figures (PS files). The paper will appear in Journal of
Physics: Condensed Matter, volume 11, issue 11 (cover date 22 March 1999) on
pages 83 - 8
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
Improved convergence of scattering calculations in the oscillator representation
The Schr\"odinger equation for two and tree-body problems is solved for
scattering states in a hybrid representation where solutions are expanded in
the eigenstates of the harmonic oscillator in the interaction region and on a
finite difference grid in the near-- and far--field. The two representations
are coupled through a high--order asymptotic formula that takes into account
the function values and the third derivative in the classical turning points.
For various examples the convergence is analyzed for various physics problems
that use an expansion in a large number of oscillator states. The results show
significant improvement over the JM-ECS method [Bidasyuk et al, Phys. Rev. C
82, 064603 (2010)]
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
(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
Vacuum Stability of the wrong sign Scalar Field Theory
We apply the effective potential method to study the vacuum stability of the
bounded from above (unstable) quantum field potential. The
stability ( and the mass renormalization
( conditions force the effective
potential of this theory to be bounded from below (stable). Since bounded from
below potentials are always associated with localized wave functions, the
algorithm we use replaces the boundary condition applied to the wave functions
in the complex contour method by two stability conditions on the effective
potential obtained. To test the validity of our calculations, we show that our
variational predictions can reproduce exactly the results in the literature for
the -symmetric theory. We then extend the applications
of the algorithm to the unstudied stability problem of the bounded from above
scalar field theory where classical analysis prohibits the
existence of a stable spectrum. Concerning this, we calculated the effective
potential up to first order in the couplings in space-time dimensions. We
find that a Hermitian effective theory is instable while a non-Hermitian but
-symmetric effective theory characterized by a pure imaginary
vacuum condensate is stable (bounded from below) which is against the classical
predictions of the instability of the theory. We assert that the work presented
here represents the first calculations that advocates the stability of the
scalar potential.Comment: 21pages, 12 figures. In this version, we updated the text and added
some 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
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