4,808 research outputs found
Spatial search in a honeycomb network
The spatial search problem consists in minimizing the number of steps
required to find a given site in a network, under the restriction that only
oracle queries or translations to neighboring sites are allowed. In this paper,
a quantum algorithm for the spatial search problem on a honeycomb lattice with
sites and torus-like boundary conditions. The search algorithm is based on
a modified quantum walk on a hexagonal lattice and the general framework
proposed by Ambainis, Kempe and Rivosh is used to show that the time complexity
of this quantum search algorithm is .Comment: 10 pages, 2 figures; Minor typos corrected, one Reference added.
accepted in Math. Structures in Computer Science, special volume on Quantum
Computin
Hexagonal spiral growth in the absence of a substrate
Experiments on the formation of spiraling hexagons (350 - 1000 nm in width)
from a solution of nanoparticles are presented. Transmission electron
microscopy images of the reaction products of chemically synthesized cadmium
nanocrystals indicate that the birth of the hexagons proceeds without
assistance from static screw or edge dislocatons, that is, they spiral without
constraints provided by an underlying substrate. Instead, the apparent growth
mechanism relies on what we believe is a dynamical dislocation identified as a
dense aggregate of small nanocrystals that straddles the spiraling hexagon at
the crystal surface. This nanocrystal bundle, which we term the "feeder", also
appears to release nanocrystals into the spiral during the growth process.Comment: 4 pages, 5 figure
The Books of Chronicles
The books of the Chronicles : critical edition of the Hebrew text printed in colors exhibiting the composite structure of the book / with notes by R. Kittel ; English translation of the notes by B.W. Bacon.https://scholar.csl.edu/ebooks/1014/thumbnail.jp
Spatial quantum search in a triangular network
The spatial search problem consists in minimizing the number of steps
required to find a given site in a network, under the restriction that only
oracle queries or translations to neighboring sites are allowed. We propose a
quantum algorithm for the spatial search problem on a triangular lattice with N
sites and torus-like boundary conditions. The proposed algortithm is a special
case of the general framework for abstract search proposed by Ambainis, Kempe
and Rivosh [AKR05] (AKR) and Tulsi [Tulsi08], applied to a triangular network.
The AKR-Tulsi formalism was employed to show that the time complexity of the
quantum search on the triangular lattice is O(sqrt(N logN)).Comment: 10 pages, 4 Postscript figures, uses sbc-template.sty, appeared in
Annals of WECIQ 2010, III Workshop of Quantum Computation and Quantum
Informatio
Effect of disorder studied with ferromagnetic resonance for arrays of tangentially magnetized sub-micron Permalloy discs fabricated by nanosphere lithography
Tangentially magnetized trigonal arrays of sub-micron Permalloy discs are
characterized with ferromagnetic resonance to determine the possible
contributions to frequency and linewidth from array disorder. Each array is
fabricated by a water-surface self-assembly lithographic technique, and
consists of a large trigonal array of 700 nm diameter magnetic discs. Each
array is characterized by a different degree of ordering. Two modes are present
in the ferromagnetic resonance spectra: a large amplitude, `fundamental' mode
and a lower amplitude mode at higher field. Angular dependence of the resonance
field in a very well ordered array is found to be negligible for both modes.
The relationship between resonance frequency and applied magnetic field is
found to be uncorrelated with array disorder. Linewidth is found to increase
with increasing array disorder
Quantized Lattice Dynamic Effects on the Spin-Peierls Transition
The density matrix renormalization group method is used to investigate the
spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We
use a phonon spectrum that interpolates between a gapped, dispersionless
(Einstein) limit to a gapless, dispersive (Debye) limit. A variety of
theoretical probes are used to determine the quantum phase transition,
including energy gap crossing, a finite size scaling analysis, bond order
auto-correlation functions, and bipartite quantum entanglement. All these
probes indicate that in the antiadiabatic phonon limit a quantum phase
transition of the Berezinskii-Kosterlitz-Thouless type is observed at a
non-zero spin-phonon coupling, . An extrapolation from the
Einstein limit to the Debye limit is accompanied by an increase in for a fixed optical () phonon gap. We therefore conclude that the
dimerized ground state is more unstable with respect to Debye phonons, with the
introduction of phonon dispersion renormalizing the effective spin-lattice
coupling for the Peierls-active mode. We also show that the staggered spin-spin
and phonon displacement order parameters are unreliable means of determining
the transition.Comment: To be published in Phys. Rev.
Dynamic Kerr effect responses in the Terahertz-range
Dynamic Kerr effect measurements provide a simple realization of a nonlinear
experiment. We propose a field-off experiment where an electric field of one or
several sinusoidal cycles is applied to a sample in thermal equilibrium.
Afterwards, the evolution of the polarizability is measured. If such an
experiment is performed in the Terahertz-range it might provide valuable
information about the low-frequency dynamics in disordered systems. We treat
these dynamics in terms of a Brownian oscillator model and calculate the Kerr
effect response. It is shown that frequency-selective behaviour can be
expected. In the interesting case of underdamped vibrational motion we find
that the frequency-dependence of the phonon-damping can be determined from the
experiment. Also the behaviour of overdamped relaxational modes is discussed.
For typical glassy materials we estimate the magnitude of all relevant
quantities, which we believe to be helpful in experimental realizations.Comment: 26 pages incl. 5 figure
Universal low-temperature tricritical point in metallic ferromagnets and ferrimagnets
An earlier theory of the quantum phase transition in metallic ferromagnets is
revisited and generalized in three ways. It is shown that the mechanism that
leads to a fluctuation-induced first-order transition in metallic ferromagnets
with a low Curie temperature is valid, (1) irrespective of whether the magnetic
moments are supplied by the conduction electrons or by electrons in another
band, (2) for ferromagnets in the XY and Ising universality classes as well as
for Heisenberg ferromagnets, and (3) for ferrimagnets as well as for
ferromagnets. This vastly expands the class of materials for which a
first-order transition at low temperatures is expected, and it explains why
strongly anisotropic ferromagnets, such as UGe2, display a first-order
transition as well as Heisenberg magnets.Comment: 11pp, 2 fig
Computational study of boron nitride nanotube synthesis: how catalyst morphology stabilizes the boron nitride bond
In an attempt to understand why catalytic methods for the growth of boron
nitride nanotubes work much worse than for their carbon counterparts, we use
first-principles calculations to study the energetics of elemental reactions
forming N2, B2 and BN molecules on an iron catalyst. We observe that in the
case of these small molecules, the catalytic activity is hindered by the
formation of B2 on the iron surface. We also observe that the local morphology
of a step edge present in our nanoparticle model stabilizes the boron nitride
molecule with respect to B2 due to the ability of the step edge to offer sites
with different coordination simultaneously for nitrogen and boron. Our results
emphasize the importance of atomic steps for a high yield chemical vapor
deposition growth of BN nanotubes and may outline new directions for improving
the efficiency of the method.Comment: submitted to physical review
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