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 $N$ 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 $O(\sqrt{N \log N})$.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, $g_{\text c}$. An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in $g_{\text c}$ for a fixed optical ($q=\pi$) 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