278 research outputs found
Affine and toric hyperplane arrangements
We extend the Billera-Ehrenborg-Readdy map between the intersection lattice
and face lattice of a central hyperplane arrangement to affine and toric
hyperplane arrangements. For arrangements on the torus, we also generalize
Zaslavsky's fundamental results on the number of regions.Comment: 32 pages, 4 figure
Anisotropic exchange interaction of localized conduction-band electrons in semiconductor structures
The spin-orbit interaction in semiconductors is shown to result in an
anisotropic contribution into the exchange Hamiltonian of a pair of localized
conduction-band electrons. The anisotropic exchange interaction exists in
semiconductor structures which are not symmetric with respect to spatial
inversion, for instance in bulk zinc-blend semiconductors. The interaction has
both symmetric and antisymmetric parts with respect to permutation of spin
components. The antisymmetric (Dzyaloshinskii-Moriya) interaction is the
strongest one. It contributes significantly into spin relaxation of localized
electrons; in particular, it governs low-temperature spin relaxation in n-GaAs
with the donor concentration near 10^16cm-3. The interaction must be allowed
for in designing spintronic devices, especially spin-based quantum computers,
where it may be a major source of decoherence and errors
Spin and energy transfer in nanocrystals without transport of charge
We describe a mechanism of spin transfer between individual quantum dots that
does not require tunneling. Incident circularly-polarized photons create
inter-band excitons with non-zero electron spin in the first quantum dot. When
the quantum-dot pair is properly designed, this excitation can be transferred
to the neighboring dot via the Coulomb interaction with either {\it
conservation} or {\it flipping} of the electron spin. The second dot can
radiate circularly-polarized photons at lower energy. Selection rules for spin
transfer are determined by the resonant conditions and by the strong spin-orbit
interaction in the valence band of nanocrystals. Coulomb-induced energy and
spin transfer in pairs and chains of dots can become very efficient under
resonant conditions. The electron can preserve its spin orientation even in
randomly-oriented nanocrystals.Comment: 13 pages, 3 figure
Magnetic field dependence of the exciton energy in a quantum disk
The groundstate energy and binding energy of an exciton, confined in a^M
quantum disk, are calculated as a function of an external magnetic field. The
confinement potential is a hard wall of finite height. The diamagnetic shift is
investigated for magnetic fields up to 40. Our results are applied to
self-assembled quantum dots and very good
agreement with experiments is obtained. Furthermore, we investigated the
influence of the dot size on the diamagnetic shift by changing the disk radius.
The exciton excited states are found as a function of the magnetic field. The
relative angular momentum is not a quantum number and changes with the magnetic
field strength.Comment: 10 pages, 17 figure
Sub-microsecond correlations in photoluminescence from InAs quantum dots
Photon correlation measurements reveal memory effects in the optical emission
of single InAs quantum dots with timescales from 10 to 800 ns. With above-band
optical excitation, a long-timescale negative correlation (antibunching) is
observed, while with quasi-resonant excitation, a positive correlation
(blinking) is observed. A simple model based on long-lived charged states is
presented that approximately explains the observed behavior, providing insight
into the excitation process. Such memory effects can limit the internal
efficiency of light emitters based on single quantum dots, and could also be
problematic for proposed quantum-computation schemes.Comment: 8 pages, 8 figure
Molecular spintronics: Coherent spin transfer in coupled quantum dots
Time-resolved Faraday rotation has recently demonstrated coherent transfer of
electron spin between quantum dots coupled by conjugated molecules. Using a
transfer Hamiltonian ansatz for the coupled quantum dots, we calculate the
Faraday rotation signal as a function of the probe frequency in a pump-probe
setup using neutral quantum dots. Additionally, we study the signal of one
spin-polarized excess electron in the coupled dots. We show that, in both
cases, the Faraday rotation angle is determined by the spin transfer
probabilities and the Heisenberg spin exchange energy. By comparison of our
results with experimental data, we find that the transfer matrix element for
electrons in the conduction band is of order 0.08 eV and the spin transfer
probabilities are of order 10%.Comment: 13 pages, 6 figures; minor change
Light scattering from disordered overlayers of metallic nanoparticles
We develop a theory for light scattering from a disordered layer of metal
nanoparticles resting on a sample. Averaging over different disorder
realizations is done by a coherent potential approximation. The calculational
scheme takes into account effects of retardation, multipole excitations, and
interactions with the sample. We apply the theory to a system similar to the
one studied experimentally by Stuart and Hall [Phys. Rev. Lett. {\bf 80}, 5663
(1998)] who used a layered Si/SiO/Si sample. The calculated results agree
rather well with the experimental ones. In particular we find conspicuous
maxima in the scattering intensity at long wavelengths (much longer than those
corresponding to plasmon resonances in the particles). We show that these
maxima have their origin in interference phenomena in the layered sample.Comment: 19 pages, 12 figure
Spin-based all-optical quantum computation with quantum dots: understanding and suppressing decoherence
We present an all-optical implementation of quantum computation using
semiconductor quantum dots. Quantum memory is represented by the spin of an
excess electron stored in each dot. Two-qubit gates are realized by switching
on trion-trion interactions between different dots. State selectivity is
achieved via conditional laser excitation exploiting Pauli exclusion principle.
Read-out is performed via a quantum-jump technique. We analyze the effect on
our scheme's performance of the main imperfections present in real quantum
dots: exciton decay, hole mixing and phonon decoherence. We introduce an
adiabatic gate procedure that allows one to circumvent these effects, and
evaluate quantitatively its fidelity
Linear square-mass trajectories of radially and orbitally excited hadrons in holographic QCD
We consider a new approach towards constructing approximate holographic duals
of QCD from experimental hadron properties. This framework allows us to derive
a gravity dual which reproduces the empirically found linear square-mass
trajectories of universal slope for radially and orbitally excited hadrons.
Conformal symmetry breaking in the bulk is exclusively due to infrared
deformations of the anti-de Sitter metric and governed by one free mass scale
proportional to Lambda_QCD. The resulting background geometry exhibits dual
signatures of confinement and provides the first examples of holographically
generated linear trajectories in the baryon sector. The predictions for the
light hadron spectrum include new relations between trajectory slopes and
ground state masses and are in good overall agreement with experiment.Comment: 33 pages, 5 figures, updated to the extended version published in
JHEP, vector meson bulk potential and metric corrected, comments and
references added, phenomenology and conclusions unchange
Hopf algebras and Markov chains: Two examples and a theory
The operation of squaring (coproduct followed by product) in a combinatorial
Hopf algebra is shown to induce a Markov chain in natural bases. Chains
constructed in this way include widely studied methods of card shuffling, a
natural "rock-breaking" process, and Markov chains on simplicial complexes.
Many of these chains can be explictly diagonalized using the primitive elements
of the algebra and the combinatorics of the free Lie algebra. For card
shuffling, this gives an explicit description of the eigenvectors. For
rock-breaking, an explicit description of the quasi-stationary distribution and
sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes
will only appear on the version on Amy Pang's website, the arXiv version will
not be updated.
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