Two-mode entanglement in two-component Bose-Einstein condensates

We study the generation of two-mode entanglement in a two-component Bose-Einstein condensate trapped in a double-well potential. By applying the Holstein-Primakoff transformation, we show that the problem is exactly solvable as long as the number of excitations due to atom-atom interactions remains low. In particular, the condensate constitutes a symmetric Gaussian system, thereby enabling its entanglement of formation to be measured directly by the fluctuations in the quadratures of the two constituent components [Giedke {\it et al.}, Phys. Rev. Lett. {\bf 91}, 107901 (2003)]. We discover that significant two-mode squeezing occurs in the condensate if the interspecies interaction is sufficiently strong, which leads to strong entanglement between the two components.Comment: 22 pages, 4 figure

Multiscale Shannon’s entropy modelling of orientation and distance in steel fiber Micro-Tomography data

This work is concerned with the modelling and analysis of the orientation and distance between steel fibers in X-ray Micro-Tomography (XCT) data. The advantage of combining both orientation and separation in a model is that it helps provide a detailed understanding of how the steel fibers are arranged, which is easy to compare. The developed models are designed to summarise the randomness of the orientation distribution of the steel fibers both locally and across an entire volume based on multiscale entropy. Theoretical modelling, simulation and application to real imaging data are shown here. The theoretical modelling of multiscale entropy for orientation includes a proof showing the final form of the multiscale taken over a linear range of scales. A series of image processing operations are also included to overcome interslice connectivity issues to help derive the statistical descriptions of the orientation distributions of the steel fibers. The results demonstrate that multiscale entropy provides unique insights into both simulated and real imaging data of steel fiber reinforced concrete

Some considerations concerning the challenge of incorporating social variables into epidemiological models of infectious disease transmission

Incorporation of ‘social’ variables into epidemiological models remains a challenge. Too much detail and models cease to be useful; too little and the very notion of infection —a highly social process in human populations—may be considered with little reference to the social. The French sociologist Emile Durkheim proposed that the scientific study of society required identification and study of ‘social currents.’ Such ‘currents’ are what we might today describe as ‘emergent properties,’ specifiable variables appertaining to individuals and groups, which represent the perspectives of social actors as they experience the environment in which they live their lives. Here we review the ways in which one particular emergent property, hope, relevant to a range of epidemiological situations, might be used in epidemiological modelling of infectious diseases in human populations. We also indicate how such an approach might be extended to include a range of other potential emergent properties to repre

Nano-Scale Hydroxyapatite: Synthesis, Two-Dimensional Transport Experiments, and Application for Uranium Remediation

Synthetic nano-scale hydroxyapatite (NHA) was prepared and characterized using X-ray diffraction (XRD) and scanning electron microscopy (SEM) methods. The XRD data confirmed that the crystalline structure and chemical composition of NHA correspond to Ca5OH(PO4)3. The SEM data confirmed the size of NHA to be less than 50 nm. A two-dimensional physical model packed with saturated porous media was used to study the transport characteristics of NHA under constant flow conditions. The data show that the transport patterns of NHA were almost identical to tracer transport patterns. This result indicates that the NHA material can move with water like a tracer, and its movement was neither retarded nor influenced by any physicochemical interactions and/or density effects. We have also tested the reactivity of NHA with 1 mg/L hexavalent uranium (U(VI)) and found that complete removal of U(VI) is possible using 0.5 g/L NHA at pH 5 to 6. Our results demonstrate that NHA has the potential to be injected as a dilute slurry for in situ treatment of U(VI)-contaminated groundwater systems

Multiqubit symmetric states with high geometric entanglement

We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement behaves asymptotically for large N. We show that much higher geometric entanglement with improved asymptotical behavior can be obtained in comparison with the highly entangled balanced Dicke states studied previously. We also derive an upper bound for the geometric measure of entanglement of symmetric states. The connection with the quantumness of a state is discussed

Nano-Scale Hydroxyapatite: Synthesis, Two-Dimensional Transport Experiments, and Application for Uranium Remediation

Synthetic nano-scale hydroxyapatite (NHA) was prepared and characterized using X-ray diffraction (XRD) and scanning electron microscopy (SEM) methods. The XRD data confirmed that the crystalline structure and chemical composition of NHA correspond to Ca5OH(PO4)3. The SEM data confirmed the size of NHA to be less than 50 nm. A two-dimensional physical model packed with saturated porous media was used to study the transport characteristics of NHA under constant flow conditions. The data show that the transport patterns of NHA were almost identical to tracer transport patterns. This result indicates that the NHA material can move with water like a tracer, and its movement was neither retarded nor influenced by any physicochemical interactions and/or density effects. We have also tested the reactivity of NHA with 1 mg/L hexavalent uranium (U(VI)) and found that complete removal of U(VI) is possible using 0.5 g/L NHA at pH 5 to 6. Our results demonstrate that NHA has the potential to be injected as a dilute slurry for in situ treatment of U(VI)-contaminated groundwater systems

Arrays of Cooper Pair Boxes Coupled to a Superconducting Reservoir: `Superradiance' and `Revival.'

We consider an array of Cooper Pair Boxes, each of which is coupled to a superconducting reservoir by a capacitive tunnel junction. We discuss two effects that probe not just the quantum nature of the islands, but also of the superconducting reservoir coupled to them. These are analogues to the well-known quantum optical effects `superradiance,' and `revival.' When revival is extended to multiple systems, we find that `entanglement revival' can also be observed. In order to study the above effects, we utilise a highly simplified model for these systems in which all the single-electron energy eigenvalues are set to be the same (the strong coupling limit), as are the charging energies of the Cooper Pair Boxes, allowing the whole system to be represented by two large coupled quantum spins. Although this simplification is drastic, the model retains the main features necessary to capture the phenomena of interest. Given the progress in superconducting box experiments over recent years, it is possible that experiments to investigate both of these interesting quantum coherent phenomena could be performed in the forseeable future.Comment: 23 pages, 5 figures Clarifications made as recommended by refere

Lyapunov exponent of many-particle systems: testing the stochastic approach

The stochastic approach to the determination of the largest Lyapunov exponent of a many-particle system is tested in the so-called mean-field XY-Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the Lyapunov exponent to a few statistical properties of the Hessian matrix of the interaction, which can be calculated as suitable thermal averages. We have verified that there is a satisfactory quantitative agreement between theory and simulations in the disordered phases of the XY models, either with attractive or repulsive interactions. Part of the success of the theory is due to the possibility of predicting the shape of the required correlation functions, because this permits the calculation of correlation times as thermal averages.Comment: 11 pages including 6 figure

Energy absorption by "sparse" systems: beyond linear response theory

The analysis of the response to driving in the case of weakly chaotic or weakly interacting systems should go beyond linear response theory. Due to the "sparsity" of the perturbation matrix, a resistor network picture of transitions between energy levels is essential. The Kubo formula is modified, replacing the "algebraic" average over the squared matrix elements by a "resistor network" average. Consequently the response becomes semi-linear rather than linear. Some novel results have been obtained in the context of two prototype problems: the heating rate of particles in Billiards with vibrating walls; and the Ohmic Joule conductance of mesoscopic rings driven by electromotive force. Respectively, the obtained results are contrasted with the "Wall formula" and the "Drude formula".Comment: 8 pages, 7 figures, short pedagogical review. Proceedings of FQMT conference (Prague, 2011). Ref correcte

Non-Markovian Dynamics of Entanglement for Multipartite Systems

Entanglement dynamics for a couple of two-level atoms interacting with independent structured reservoirs is studied using a non-perturbative approach. It is shown that the revival of atom entanglement is not necessarily accompanied by the sudden death of reservoir entanglement, and vice versa. In fact, atom entanglement can revive before, simultaneously or even after the disentanglement of reservoirs. Using a novel method based on the population analysis for the excited atomic state, we present the quantitative criteria for the revival and death phenomena. For giving a more physically intuitive insight, the quasimode Hamiltonian method is applied. Our quantitative analysis is helpful for the practical engineering of entanglement.Comment: 10 pages and 4 figure