Correlations in low dimensional quantum systems

In this thesis I present the work done during my PhD in the area of low dimensional quantum gases. The chapters of this thesis are self contained and represent individual projects which have been peer reviewed and accepted for publication in respected international journals. Various systems are considered, the first of which is a two particle model which possesses an exact analytical solution. I investigate the non-classical correlations that exist between the particles as a function of the tunable properties of the system. In the second work I consider the coherences and out of equilibrium dynamics of a one-dimensional Tonks-Girardeau gas. I show how the coherence of the gas can be inferred from various properties of the reduced state and how this may be observed in experiments. I then present a model which can be used to probe a one-dimensional Fermi gas by performing a measurement on an impurity which interacts with the gas. I show how this system can be used to observe the so-called orthogonality catastrophe using modern interferometry techniques. In the next chapter I present a simple scheme to create superposition states of particles with special emphasis on the NOON state. I explore the effect of inter-particle interactions in the process and then characterise the usefulness of these states for interferometry. Finally I present my contribution to a project on long distance entanglement generation in ion chains. I show how carefully tuning the environment can create decoherence-free subspaces which allows one to create and preserve entanglement.

Proteomic approaches to environmental stress in mussel Mytilus edulis due to emerging classes of anthropogenic pollutants

Anthropogenic pollutant chemicals pose a major threat to aquatic organisms. There is a need for more research on emerging categories of environmental chemicals such as nanomaterials, endocrine disruptors and pharmaceuticals. Proteomics offers options and advantages for early warning of alterations in environmental quality by detecting sub-lethal changes in sentinel species such as the mussel, Mytilus edulis. This thesis aimed to compare the potential of traditional biomarkers (such as enzyme activity measurement) and newer redox proteomic approaches. Environmental proteomics, especially a redox proteomics toolbox, may be a novel way to study pollutant effects on organisms which can also yield information on risks to human health. In particular, it can probe subtle biochemical changes at sub-lethal concentrations and thus offer novel insights to toxicity mechanisms. In the first instance, the present research involved a field-study in three stations in Cork Harbour, Ireland (Haulbowline, Ringaskiddy and Douglas) compared to an outharbour control site in Bantry Bay, Ireland. Then, further research was carried out to detect effects of anthropogenic pollution on selected chemicals. Diclofenac is an example of veterinary and human pharmaceuticals, an emerging category of chemical pollutants, with potential to cause serious toxicity to non-target organisms. A second chemical used for this study was copper which is a key source of contamination in marine ecosystems. Thirdly, bisphenol A is a major anthropogenic chemical mainly used in polycarbonate plastics manufacturing that is widespread in the environment. It is also suspected to be an endocrine disruptor. Effects on the gill, the principal feeding organ of mussels, were investigated in particular. Effects on digestive gland were also investigated to compare different outcomes from each tissue. Across the three anthropogenic chemicals studied (diclofenac, copper and bisphenol A), only diclofenac exposure did not show any significant difference towards glutathione transferase (GST) responses. Meanwhile, copper and bisphenol A significantly increased GST in gill. Glutathione reductase (GR) enzyme analysis revealed that all three chemicals have significant responses in gill. Catalase activity showed significant differences in digestive gland exposed to diclofenac and gills exposed to bisphenol A. This study focused then on application of redox proteomics; the study of the oxidative modification of proteins, to M. edulis. Thiol proteins were labelled with 5-iodoacetamidofluorescein prior to one-dimensional and two-dimensional electrophoresis. This clearly revealed some similarities on a portion of the redox proteome across chemical exposures indicating where toxicity mechanism may be common and where effects are unique to a single treatment. This thesis documents that proteomics is a robust tool to provide valuable insights into possible mechanisms of toxicity of anthropogenic contaminants in M. edulis. It is concluded that future research should focus on gill tissue, on protein thiols and on key individual proteins discovered in this study such as calreticulin and arginine kinase which have not previously been considered as biomarkers in aquatic toxicology prior to this study.

Restoration of optical objects using regularization

Using the regularization theory for improperly posed problems, we discuss object restoration beyond the diffraction limit in the presence of noise. Only the case of one-dimensional coherent objects is considered. We focus attention n the estimation of the error on the restored objects, and we show that, in most realistic cases, it is at best proportional to an inverse power of

A coarse grid extraction of sound signals for computational aeroacoustics

Sound waves are propagating pressure fluctuations, which are typically several orders of magnitude smaller than the pressure variations in the flow field that account for flow acceleration. On the other hand, these fluctuations travel at the speed of sound in the medium, not as a transported fluid quantity. Due to the above two properties, the Reynolds averaged Navier–Stokes equations do not resolve the acoustic fluctuations. This paper discusses a defect correction method for this type of multi-scale problems in aeroacoustics. Numerical examples in one dimensional and two dimensional are used to illustrate the concept. Copyright (C) 2002 John Wiley & Sons, Ltd.

A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling

1. A first step in the analysis of complex movement data often involves discretisation of the path into a series of step-lengths and turns, for example in the analysis of specialised random walks, such as Lévy flights. However, the identification of turning points, and therefore step-lengths, in a tortuous path is dependent on ad-hoc parameter choices. Consequently, studies testing for movement patterns in these data, such as Lévy flights, have generated debate. However, studies focusing on one-dimensional (1D) data, as in the vertical displacements of marine pelagic predators, where turning points can be identified unambiguously have provided strong support for Lévy flight movement patterns. 2. Here, we investigate how step-length distributions in 3D movement patterns would be interpreted by tags recording in 1D (i.e. depth) and demonstrate the dimensional symmetry previously shown mathematically for Lévy-flight movements. We test the veracity of this symmetry by simulating several measurement errors common in empirical datasets and find Lévy patterns and exponents to be robust to low-quality movement data. 3. We then consider exponential and composite Brownian random walks and show that these also project into 1D with sufficient symmetry to be clearly identifiable as such. 4. By extending the symmetry paradigm, we propose a new methodology for step-length identification in 2D or 3D movement data. The methodology is successfully demonstrated in a re-analysis of wandering albatross Global Positioning System (GPS) location data previously analysed using a complex methodology to determine bird-landing locations as turning points in a Lévy walk. For this high-resolution GPS data, we show that there is strong evidence for albatross foraging patterns approximated by truncated Lévy flights spanning over 3·5 orders of magnitude. 5. Our simple methodology and freely available software can be used with any 2D or 3D movement data at any scale or resolution and are robust to common empirical measurement errors. The method should find wide applicability in the field of movement ecology spanning the study of motile cells to humans.

Time-dependent tight binding

Starting from a Lagrangian mean-field theory, a set of time-dependent tight-binding equations is derived to describe dynamically and self-consistently an interacting system of quantum electrons and classical nuclei. These equations conserve norm, total energy and total momentum. A comparison with other tight-binding models is made. A previous tight-binding result for forces on atoms in the presence of electrical current flow is generalized to the time-dependent domain and is taken beyond the limit of local charge neutrality.

Solving the advection-dispersion equation using the discrete puff particle method

A flexible, mass-conservative numerical technique for solving the advection-dispersion equation for miscible contaminant transport is presented. The method combines features of puff transport models from air pollution studies with features from the random walk particle method used in water resources studies, providing a deterministic time-marching algorithm which is independent of the grid Peclet number and scales from one to higher dimensions simply. The concentration field is discretised into a number of particles, each of which is treated as a point release which advects and disperses over the time interval. The dispersed puff is itself discretised into a spatial distribution of particles whose masses can be pre-calculated. Concentration within the simulation domain is then calculated from the mass distribution as an average over some small volume. Comparison with analytical solutions for a one-dimensional fixed-duration concentration pulse and for two-dimensional transport in an axisymmetric flow field indicate that the algorithm performs well. For a given level of accuracy the new method has lower computation times than the random walk particle method.

Imaging of dipole sources and transfer of modulated signals using phase conjugating lens techniques

The authors discuss the imaging properties and transfer of amplitude and phase-modulated signals through a phase conjugating lens (PCL). The authors outline the mechanisms of the near-field and far-field subwavelength imaging of Hertzian dipole sources using PCL, particularly the authors show that one-dimensional subwavelength resolution of multiple sources is possible in the far-field using a PCL augmented with specially designed scatterers located in both the adjacent vicinity of the sources and in the mirror symmetric positions in the image plane. These scatterers enable evanescent-to-propagating spectrum and its dual, propagating-to-evanescent, field conversion. Thus, the subwavelength information encoded into propagating waves on the source side can be extracted on the image side. Next, for the first time the transfer of amplitude and phase modulated signals through a PCL augmented with evanescent-to-propagating spectrum conversion is discussed and it has been demonstrated that multiple amplitude or phase modulated dipole sources can be distinguished in the far-field with subwavelength resolution without the necessity for numerical post-processing of the received data. From the study conducted here, it is concluded that a system of transmitters/receivers augmented with a PCL and appropriate scatterers operates without the need for any numerical processing of the receive data in order to separate channel information from very close proximity stations.

Nonlinear modulation of transverse dust lattice waves in complex plasma crystals

The occurrence of the modulational instability in transverse dust lattice waves propagating in a one-dimensional dusty plasma crystal is investigated. The amplitude modulation mechanism, which is related to the intrinsic nonlinearity of the sheath electric field, is shown to destabilize the carrier wave under certain conditions, possibly leading to the formation of localized envelope excitations. Explicit expressions for the instability growth rate and threshold are presented and discussed. (C) 2004 American Institute of Physics.

Ground state of low-dimensional dipolar gases: Linear and zigzag chains

We study the ground-state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the quantum system is performed numerically with Monte Carlo techniques and shows that the quantum fluctuations smoothen the transition and make it completely disappear in a gas phase. These predictions could be experimentally tested and would allow one to reveal the effect of zero-point motion on self-organized mesoscopic structures of matter waves, such as the transverse pattern of the zigzag chain.

Extreme ultraviolet line emission at 24.7 nm from Li-like nitrogen plasma produced by a short KrF excimer laser pulse

Recently using KrF high power laser (248 nm; 350 fs; 5.0x10(16) W/cm(2)) in the Rutherford Appleton Laboratory an experimental search for recombination extreme ultraviolet (XUV) laser action in Li-like nitrogen ions was performed. To understand the experimental results of line emission at 24.7 nm in the 3d(5/2)-2p(3/2) transition of the Li-like nitrogen ion a simulation was undertaken using a one-dimensional Lagrangian hydrodynamic code. From the simulation results, we confirmed that there was nonlinear dependence of spectral line emission on the gas density which was well matched to the experimental results. Only a six times increase of the 24.7 nm emission intensity was obtained when the plasma length was increased 1000 times from 1 mu m as an optically thin case to 1 mm. Also, the spatial profile of the electron density and temperature was obtained and the electron temperature was about 40-50 eV which was too high for the optical field ionization x-ray lasing. We could not find evidence of x-ray laser gain. (C) 1996 American Institute of Physics.

Welfare regime and social class variation in poverty and economic vulnerability in Europe: an analysis of EU-SILC

In this paper we address a set of interrelated issues. These comprise increasing concerns about reliance on nationally based income poverty measures in the context of EU enlargement, the relative merits of one-dimensional versus multidimensional approaches to poverty and social exclusion and the continuing relevance of class-based explanations of life chances. When identifying economically vulnerable groups we find that, contrary to the situation with national income poverty measures, levels of vulnerability vary systematically across welfare regimes. The multidimensional profile of the economically vulnerable sharply differentiates them from the remainder of the population. While they are also characterised by distinctively higher levels of multiple deprivation, a substantial majority of the economically vulnerable are not exposed to such deprivation. Unlike the national relative income approach, the focus on economic vulnerability reveals a pattern of class differentiation that is not dominated by the contrast between the self-employed and all others. In contrast to a European-wide relative income approach, it also simultaneously captures the fact that absolute levels of vulnerability are distinctively higher among the lower social classes in the less comprehensive and generous welfare regimes while class relativities are significantly sharper at the other end of the spectrum.

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.

Adaptive calibration of a three-microphone system for acoustic waveguide characterization under time-varying conditions

The pressure and velocity field in a one-dimensional acoustic waveguide can be sensed in a non-intrusive manner using spatially distributed microphones. Experimental characterization with sensor arrangements of this type has many applications in measurement and control. This paper presents a method for measuring the acoustic variables in a duct under fluctuating propagation conditions with specific focus on in-system calibration and tracking of the system parameters of a three-microphone measurement configuration. The tractability of the non-linear optimization problem that results from taking a parametric approach is investigated alongside the influence of extraneous measurement noise on the parameter estimates. The validity and accuracy of the method are experimentally assessed in terms of the ability of the calibrated system to separate the propagating waves under controlled conditions. The tracking performance is tested through measurements with a time-varying mean flow, including an experiment conducted under propagation conditions similar to those in a wind instrument during playing.

Design of a radio frequency heated isothermal micro-trickle bed reactor

A near-isothermal micro-trickle bed reactor operated under radio frequency heating was developed. The reactor bed was packed with nickel ferrite micro-particles of 110. μm diameter, generating heat by the application of RF field at 180. kHz. Hydrodynamics in a co-current configuration was analysed and heat transfer rates were determined at temperature ranging from 55 to 100. °C. A multi-zone reactor bed of several heating and catalytic zones was proposed in order to achieve near-isothermal operations. Exact positioning, number of the heating zones and length of the heating zones composed of a mixture of nickel ferrite and a catalyst were determined by solving a one dimensional model of heat transfer by conduction and convection. The conductive losses contributed up to 30% in the total thermal losses from the reactor. Three heating zones were required to obtain an isothermal length of 50. mm with a temperature non-uniformity of 2. K. A good agreement between the modelling and experimental results was obtained for temperature profiles of the reactor. © 2013 Elsevier B.V.