37 research outputs found

### Magnetic dipole and electric quadrupole responses of elliptic quantum dots in magnetic fields

The magnetic dipole (M1) and electric quadupole (E2) responses of
two-dimensional quantum dots with an elliptic shape are theoretically
investigated as a function of the dot deformation and applied static magnetic
field. Neglecting the electron-electron interaction we obtain analytical
results which indicate the existence of four characteristic modes, with
different $B$-dispersion of their energies and associated strengths.
Interaction effects are numerically studied within the time-dependent
local-spin-density theory, assessing the validity of the non-interacting
picture.Comment: 11 pages, 3 GIF figure

### Spin-orbit effects on the Larmor dispersion relation in GaAs quantum wells

We have studied the relevance of spin-orbit coupling to the dispersion 00009
relation of the Larmor resonance observed in inelastic light scattering and
electron-spin resonance experiments on GaAs quantum wells. We show that the
spin-orbit interaction, here described by a sum of Dresselhaus and
Bychkov-Rashba terms, couples Zeeman and spin-density excitations. We have
evaluated its contribution to the spin splitting as a function of the magnetic
field $B$, and have found that in the small $B$ limit, the spin-orbit
interaction does not contribute to the spin splitting, whereas at high magnetic
fields it yields a $B$ independent contribution to the spin splitting given by
$2(\lambda_R^2-\lambda_D^2)$, with $\lambda_{R,D}$ being the intensity of the
Bychkov-Rashba and Dresselhaus spin-orbit terms.Comment: To be published in Physical Review

### Satisfiability of Non-Linear Transcendental Arithmetic as a Certificate Search Problem

For typical first-order logical theories, satisfying assignments have a
straightforward finite representation that can directly serve as a certificate
that a given assignment satisfies the given formula. For non-linear real
arithmetic with transcendental functions, however, no general finite
representation of satisfying assignments is available. Hence, in this paper, we
introduce a different form of satisfiability certificate for this theory,
formulate the satisfiability verification problem as the problem of searching
for such a certificate, and show how to perform this search in a systematic
fashion. This does not only ease the independent verification of results, but
also allows the systematic design of new, efficient search techniques.
Computational experiments document that the resulting method is able to prove
satisfiability of a substantially higher number of benchmark problems than
existing methods

### Orbital current mode in elliptical quantum dots

An orbital current mode peculiar to deformed quantum dots is theoretically
investigated; first by using a simple model that allows to interpret
analytically its main characteristics, and second, by numerically solving the
microscopic equations of time evolution after an initial perturbation within
the time-dependent local-spin-density approximation. Results for different
deformations and sizes are shown.Comment: 4 REVTEX pages, 4 PDF figures, accepted in PRB:R

### Wave-vector dependence of spin and density multipole excitations in quantum dots

We have employed time-dependent local-spin density functional theory to
analyze the multipole spin and charge density excitations in GaAs-AlGaAs
quantum dots. The on-plane transferred momentum degree of freedom has been
taken into account, and the wave-vector dependence of the excitations is
discussed. In agreement with previous experiments, we have found that the
energies of these modes do not depend on the transferred wave-vector, although
their intensities do. Comparison with a recent resonant Raman scattering
experiment [C. Sch\"uller et al, Phys. Rev. Lett {\bf 80}, 2673 (1998)] is
made. This allows to identify the angular momentum of several of the observed
modes as well as to reproduce their energies.Comment: 14 pages in REVTEX and 14 postscript figure

### Wave-vector dependence of spin and density multipole excitations in quantum dots

We have employed time-dependent local-spin density functional theory to
analyze the multipole spin and charge density excitations in GaAs-AlGaAs
quantum dots. The on-plane transferred momentum degree of freedom has been
taken into account, and the wave-vector dependence of the excitations is
discussed. In agreement with previous experiments, we have found that the
energies of these modes do not depend on the transferred wave-vector, although
their intensities do. Comparison with a recent resonant Raman scattering
experiment [C. Sch\"uller et al, Phys. Rev. Lett {\bf 80}, 2673 (1998)] is
made. This allows to identify the angular momentum of several of the observed
modes as well as to reproduce their energies.Comment: 14 pages in REVTEX and 14 postscript figure

### Spin-orbit effects in GaAs quantum wells: Interplay between Rashba, Dresselhaus, and Zeeman interactions

The interplay between Rashba, Dresselhaus and Zeeman interactions in a
quantum well submitted to an external magnetic field is studied by means of an
accurate analytical solution of the Hamiltonian, including electron-electron
interactions in a sum rule approach. This solution allows to discuss the
influence of the spin-orbit coupling on some relevant quantities that have been
measured in inelastic light scattering and electron-spin resonance experiments
on quantum wells. In particular, we have evaluated the spin-orbit contribution
to the spin splitting of the Landau levels and to the splitting of charge- and
spin-density excitations. We also discuss how the spin-orbit effects change if
the applied magnetic field is tilted with respect to the direction
perpendicular to the quantum well.Comment: 26 pages (with 3 figures included

### Multipole modes and spin features in the Raman spectrum of nanoscopic quantum rings

We present a systematic study of ground state and spectroscopic properties of many-electron nanoscopic quantum rings. Addition energies at zero magnetic field (B) and electrochemical potentials as a function of B are given for a ring hosting up to 24 electrons. We find discontinuities in the excitation energies of multipole spin and charge density modes, and a coupling between the charge and spin density responses that allow to identify the formation of ferromagnetic ground states in narrow magnetic field regions. These effects can be observed in Raman experiments, and are related to the fractional Aharonov-Bohm oscillations of the energy and of the persistent current in the rin