Quantum State Transfer in Spin-1 Chains

We study the transfer of quantum information through a Heisenberg spin-1 chain prepared in its ground state. We measure the efficiency of such a quantum channel {\em via} the fidelity of retrieving an arbitrarily prepared state and {\em via} the transfer of quantum entanglement. The Heisenberg spin-1 chain has a very rich quantum phase diagram. We show that the phase boundaries are reflected in sharp variations of the transfer efficiency. In the vicinity of the border between the dimer and the ferromagnetic phase (in the conjectured spin-nematic region), we find strong indications for a qualitative change of the excitation spectrum. Moreover, we identify two regions of the phase diagram which give rise to particularly high transfer efficiency; the channel might be non-classical even for chains of arbitrary length, in contrast to spin-1/2 chains.Comment: 4 pages, 4 figures, published versio

Velocity and Friction Characteristics of Laminar Viscous Boundary-layer and Channel Flow over Surfaces with Ejection or Suction

National Advisory Committee for Aeronautics Technical Note 4102 Information collected from the referenced literature and supplemented by new solutions is presented on the flow characteristics - velocity field, pressure drop, and friction - for steady, fully developed laminar flow through a duct consisting of two parallel walls, for flow through tubes with circular cross section, and for boundary-layer flow over infinite wedges. It is assumed that the fluid either is ejected through the porous walls into the main flow or is removed from the main flow by suction. The properties of the fluid both in the main flow and in passing through the porous walls are assumed constant, identical, and incompressible. In order to determine the extent to which the boundary conditions imposed on the flow by the various geometries influence the flow characteristics, dimensionless parameters common to both channel and boundary-layer flow (channel flow is flow with bounding walls, e.g., a tube) were developed. By using these parameters to compare the various flows, the flow on surfaces with fluid ejection as well as on solid surfaces was found to depend mainly on the local boundary- layer thickness, on the pressure gradient in main -flow direction, and on the ejection rates. Whether the viscous flow is confined in a channel or unconfined in a boundary layer is of secondary importance . This finding forms the basis for general correlations and shows the conditions under which data on channel and boundary- layer flow are interchangeable; it also should behttps://thekeep.eiu.edu/archives_armstead_publications/1001/thumbnail.jp

Reconstruction of the two-dimensional gravitational potential of galaxy clusters from X-ray and Sunyaev-Zel'dovich measurements

The mass of galaxy clusters is not a direct observable, nonetheless it is commonly used to probe cosmological models. Based on the combination of all main cluster observables, that is, the X-ray emission, the thermal Sunyaev-Zel'dovich (SZ) signal, the velocity dispersion of the cluster galaxies, and gravitational lensing, the gravitational potential of galaxy clusters can be jointly reconstructed. We derive the two main ingredients required for this joint reconstruction: the potentials individually reconstructed from the observables and their covariance matrices, which act as a weight in the joint reconstruction. We show here the method to derive these quantities. The result of the joint reconstruction applied to a real cluster will be discussed in a forthcoming paper. We apply the Richardson-Lucy deprojection algorithm to data on a two-dimensional (2D) grid. We first test the 2D deprojection algorithm on a $\beta$-profile. Assuming hydrostatic equilibrium, we further reconstruct the gravitational potential of a simulated galaxy cluster based on synthetic SZ and X-ray data. We then reconstruct the projected gravitational potential of the massive and dynamically active cluster Abell 2142, based on the X-ray observations collected with XMM-Newton and the SZ observations from the Planck satellite. Finally, we compute the covariance matrix of the projected reconstructed potential of the cluster Abell 2142 based on the X-ray measurements collected with XMM-Newton. The gravitational potentials of the simulated cluster recovered from synthetic X-ray and SZ data are consistent, even though the potential reconstructed from X-rays shows larger deviations from the true potential. Regarding Abell 2142, the projected gravitational cluster potentials recovered from SZ and X-ray data reproduce well the projected potential inferred from gravitational-lensing observations. (abridged)Comment: accepted for publication in the journal A&

Complete hierarchies of efficient approximations to problems in entanglement theory

We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multi-party entangled, (B) the minimization of expectation values of entanglement witnesses with respect to pure product states, (C) the closely related evaluation of the geometric measure of entanglement to quantify pure multi-party entanglement, (D) the test whether states are multi-party entangled on the basis of witnesses based on second moments and on the basis of linear entropic criteria, and (E) the evaluation of instances of maximal output purities of quantum channels. We show that these problems can be formulated as certain optimization problems: as polynomially constrained problems employing polynomials of degree three or less. We then apply very recently established known methods from the theory of semi-definite relaxations to the formulated optimization problems. By this construction we arrive at a hierarchy of efficiently solvable approximations to the solution, approximating the exact solution as closely as desired, in a way that is asymptotically complete. For example, this results in a hierarchy of novel, efficiently decidable sufficient criteria for multi-particle entanglement, such that every entangled state will necessarily be detected in some step of the hierarchy. Finally, we present numerical examples to demonstrate the practical accessibility of this approach.Comment: 14 pages, 3 figures, tiny modifications, version to be published in Physical Review

A model for analysis of the temperature field downstream of a heated jet injected into an isothermal crossflow at an angle of 90 deg

The temperature distribution downstream of a heated jet entering an isothermal crossflow at an angle of 90 deg is predicted using two conduction models with energy sources above the point of injection, in one case a point source and in the second a line source. The models use effective turbulent diffusivities that are determined empirically from previous measurements. Temperatures predicted by the models are compared to experimental results

The two-component giant radio halo in the galaxy cluster Abell 2142

We report on a spectral study at radio frequencies of the giant radio halo in A2142 (z=0.0909), which we performed to explore its nature and origin. A2142 is not a major merger and the presence of a giant radio halo is somewhat surprising. We performed deep radio observations with the GMRT at 608 MHz, 322 MHz, and 234 MHz and with the VLA in the 1-2 GHz band. We obtained high-quality images at all frequencies in a wide range of resolutions. The radio halo is well detected at all frequencies and extends out to the most distant cold front in A2142. We studied the spectral index in two regions: the central part of the halo and a second region in the direction of the most distant south-eastern cold front, selected to follow the bright part of the halo and X-ray emission. We complemented our observations with a preliminary LOFAR image at 118 MHz and with the re-analysis of archival VLA data at 1.4 GHz. The two components of the radio halo show different observational properties. The central brightest part has higher surface brightess and a spectrum whose steepness is similar to those of the known radio halos, i.e. $\alpha^{\rm 1.78~GHz}_{\rm 118~MHz}=1.33\pm 0.08$. The ridge, which fades into the larger scale emission, is broader in size and has considerably lower surface brightess and a moderately steeper spectrum, i.e. $\alpha^{\rm 1.78~GHz}_{\rm 118~MHz}\sim 1.5$. We propose that the brightest part of the radio halo is powered by the central sloshing in A2142, similar to what has been suggested for mini-halos, or by secondary electrons generated by hadronic collisions in the ICM. On the other hand, the steeper ridge may probe particle re-acceleration by turbulence generated either by stirring the gas and magnetic fields on a larger scale or by less energetic mechanisms, such as continuous infall of galaxy groups or an off-axis merger.Comment: 18 pages, 10 figures, 4 tables - A&A, accepte

Film cooling following injection through inclined circular tubes

Film cooling following air injection through inclined flat plate holes into turbulent boundary laye