Global quantum correlations in finite-size spin chains

We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sarandy 2011 Phys. Rev. A 84 042109), called global discord, we show that critical points can be neatly detected even for many-body systems that are not in their ground state. We consider the transverse Ising model, the cluster-Ising model where three-body couplings compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian in transverse magnetic field. These models embody our canonical examples showing the sensitivity of global quantum discord close to criticality. For the Ising model, we find a universal scaling of global discord with the critical exponents pertaining to the Ising universality class.

Dispersing Light with Surface Plasmon Polaritonic Crystals

Spectral dispersion of light on a finite-size surface plasmon polaritonic (SPP) crystal has been studied. The angular wavelength separation of one or more orders of magnitude higher than in other state-of-the-art wavelength-splitting devices available to date has been demonstrated. The two-stage process is responsible for the dispersion value, which involves conversion of the incident light into SPP Bloch modes of a nanostructure followed by the SPP Bloch waves refraction at the SPP crystal boundary. The high spectral dispersion achievable in plasmonic devices may be useful for integrated high-resolution spectroscopy in nanophotonic, optical communication and lab-on-a-chip applications.

Sub-Wavelength Profile 2-D Leaky-Wave Antennas With Two Periodic Layers

A fast and accurate analysis and synthesis technique for high-gain sub-wavelength 2-D Fabry-Perot leaky-wave antennas (LWA) consisting of two periodic metallodielectric arrays over a ground plane is presented. Full-wave method of moments (MoM) together with reciprocity is employed for the estimation of the near fields upon plane wave illumination and the extraction of the radiation patterns of the LWA. This yields a fast and rigorous tool for the characterisation of this type of antennas. A thorough convergence study for different antenna designs is presented and the operation principles of these antennas as well as the radiation characteristics are discussed. Moreover, design guidelines to tailor the antenna profile, the dimensions of the arrays as well as the antenna directivity and bandwidth are provided. A study on the radiation efficiency for antennas with different profiles is also presented and the trade off between directivity and radiation bandwidth is discussed. Numerical examples are given throughout to demonstrate the technique. A finite size antenna model is simulated using commercial software (CST Microstripes 2009) which validates the technique.

Thermal conductivity measurement of liquids in a microfluidic device

A new microfluidic-based approach to measuring liquid thermal conductivity is developed to address the requirement in many practical applications for measurements using small (microlitre) sample size and integration into a compact device. The approach also gives the possibility of high-throughput testing. A resistance heater and temperature sensor are incorporated into a glass microfluidic chip to allow transmission and detection of a planar thermal wave crossing a thin layer of the sample. The device is designed so that heat transfer is locally one-dimensional during a short initial time period. This allows the detected temperature transient to be separated into two distinct components: a short-time, purely one-dimensional part from which sample thermal conductivity can be determined and a remaining long-time part containing the effects of three-dimensionality and of the finite size of surrounding thermal reservoirs. Identification of the one-dimensional component yields a steady temperature difference from which sample thermal conductivity can be determined. Calibration is required to give correct representation of changing heater resistance, system layer thicknesses and solid material thermal conductivities with temperature. In this preliminary study, methanol/water mixtures are measured at atmospheric pressure over the temperature range 30-50A degrees C. The results show that the device has produced a measurement accuracy of within 2.5% over the range of thermal conductivity and temperature of the tests. A relation between measurement uncertainty and the geometric and thermal properties of the system is derived and this is used to identify ways that error could be further reduced.

Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains

We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix ?1, ?2, signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.

Interaction-induced correlations and non-Markovianity of quantum dynamics

We investigate the conditions under which the trace distance between two different states of a given open system increases in time due to the interaction with an environment, therefore signaling non-Markovianity. We find that the finite-time difference in trace distance is bounded by two sharply defined quantities that are strictly linked to the occurrence of system-environment correlations created throughout their interaction and affecting the subsequent evolution of the system. This allows us to shed light on the origin of non-Markovian behaviors in quantum dynamics. We best illustrate our findings by tackling two physically relevant examples: a non-Markovian dephasing mechanism that has been the focus of a recent experimental endeavor and the open-system dynamics experienced by a spin connected to a finite-size quantum spin chain.

Criticality, factorization, and long-range correlations in the anisotropic XY model

We study the long-range quantum correlations in the anisotropic XY model. By first examining the thermodynamic limit, we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. Furthermore, by considering suitably large site separations we find that these correlations obey a simple scaling behavior for finite temperatures, allowing for efficient estimation of the critical point. We also address ground-state factorization of this model by explicitly considering finite-size systems, showing its relation to the energy spectrum and explaining the persistence of the phenomenon at finite temperatures. Finally, we compute the fidelity between finite and infinite systems in order to show that remarkably small system sizes can closely approximate the thermodynamic limit.

A metapopulation model of species boundaries

The majority, if not all, species have a limited geographic range bounded by a distribution edge. Violent ecotones such as sea coasts clearly produce edges for many species; however such ecotones, while sufficient for the formation of an edge, are not always necessary. We demonstrate this by simulation in discrete time of a spatially structured finite size metapopulation subjected to a spatial gradient in per-unit-time population extinction probability together with spatially structured dispersal and recolonisation. We find that relatively sharp edges separating a homeland or main geographical range from an outland or zone of relatively sparse and ephemeral colonisation can form in gradual environmental gradients. The form and placing of the edge is an emergent property of the metapopulation dynamics. The sharpness of the edge declines with increasing dispersal distance, and is dependent on the relative scales of dispersal distance and gradient length. The space over which the edge develops is short relative to the potential species range. The edge is robust against changes in both the shape of the environmental gradient and to a lesser extent to alterations in the kind of dispersal operating. Persistence times in the absence of environmental gradients are virtually independent of the shape of the dispersal function describing migration. The common finding of bell shaped population density distributions across geographic ranges may occur without the strict necessity of a niche mediated response to a spatially autocorrelated environment.

Nonequilibrium critical scaling from quantum thermodynamics

The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully predicts the equilibrium critical exponents for the crossover length and the order parameter of the model, and, moreover, implies a new exponent for the rescaled irreversible work. By connecting the irreversible work to the two-impurity spin correlation function, our findings can be tested experimentally.

Some current problems in perovskite nano-ferroelectrics and multiferroics: kinetically-limited systems of finite lateral size

We describe some unsolved problems of current interest; these involve quantum critical points in
ferroelectrics and problems which are not amenable to the usual density functional theory, nor to
classical Landau free energy approaches (they are kinetically limited), nor even to the Landau–
Kittel relationship for domain size (they do not satisfy the assumption of infinite lateral diameter)
because they are dominated by finite aperiodic boundary conditions.

How optimal life history changes with the community size-spectrum

This paper derives optimal life histories for fishes or other animals in relation to the size spectrum of the ecological community in which they are both predators and prey. Assuming log-linear size-spectra and well known scaling laws for feeding and mortality, we first construct the energetics of the individual. From these we find, using dynamic programming, the optimal allocation of energy between growth and reproduction as well as the trade-off between offspring size and numbers. Optimal strategies were found to be strongly dependent on size spectrum slope. For steep size spectra (numbers declining rapidly with size), determinate growth was optimal and allocation to somatic growth increased rapidly with increasing slope. However, restricting reproduction to a fixed mating season changed optimal allocations to give indeterminate growth approximating a von Bertalanffy trajectory. The optimal offspring size was as small as possible given other restrictions such as newborn starvation mortality. For shallow size spectra, finite optimal maturity size required a decline in fitness for large size or age. All the results are compared with observed size spectra of fish communities to show their consistency and relevance.

Impact of finite element idealisation on the prediction of welded fuselage stiffened panel buckling

Lap joints are widely used in the manufacture of stiffened panels and influence local panel sub-component stability, defining buckling unit dimensions and boundary conditions. Using the Finite Element method it is possible to model joints in great detail and predict panel buckling behaviour with accuracy. However, when modelling large panel structures such detailed analysis becomes computationally expensive. Moreover, the impact of local behaviour on global panel performance may reduce as the scale of the modelled structure increases. Thus this study presents coupled computational and experimental analysis, aimed at developing relationships between modelling fidelity and the size of the modelled structure, when the global static load to cause initial buckling is the required analysis output. Small, medium and large specimens representing welded lap-joined fuselage panel structure are examined. Two element types, shell and solid-shell, are employed to model each specimen, highlighting the impact of idealisation on the prediction of welded stiffened panel initial skin buckling.