Multipartite entanglement in quantum spin chains

We study the occurrence of multipartite entanglement in spin chains. We show that certain genuine multipartite entangled states, namely W states, can be obtained as ground states of simple XX type ferromagnetic spin chains in a transverse magnetic field, for any number of sites. Moreover, multipartite entanglement is proven to exist even at finite temperatures. A transition from a product state to a multipartite entangled state occurs when decreasing the magnetic field to a critical value. Adiabatic passage through this point can thus lead to the generation of multipartite entanglement.Comment: 4 pages, 1 figur

Asymptotic properties of discrete linear fractional equations

In this paper we study the dynamical behavior of linear discrete-time fractional systems. The first main result is that the norm of the difference of two different solutions of a time-varying discrete-time Caputo equation tends to zero not faster than polynomially. The second main result is a complete description of the decay to zero of the trajectories of one-dimensional time-invariant stable Caputo and Riemann-Liouville equations. Moreover, we present Volterra convolution equations, that are equivalent to Caputo equations

NP-hardness of the cluster minimization problem revisited

The computational complexity of the "cluster minimization problem" is revisited [L. T. Wille and J. Vennik, J. Phys. A 18, L419 (1985)]. It is argued that the original NP-hardness proof does not apply to pairwise potentials of physical interest, such as those that depend on the geometric distance between the particles. A geometric analog of the original problem is formulated, and a new proof for such potentials is provided by polynomial time transformation from the independent set problem for unit disk graphs. Limitations of this formulation are pointed out, and new subproblems that bear more direct consequences to the numerical study of clusters are suggested.Comment: 8 pages, 2 figures, accepted to J. Phys. A: Math. and Ge

Matter-wave recombiners fro trapped Bose-Einstein condensates

Interferometry with trapped atomic Bose-Einstein condensates (BECs) requires the development of techniques to recombine the two paths of the interferometer and map the accumulated phase difference to a measurable atom number difference. We have implemented and compared two recombining procedures in a double-well-based BEC interferometer. The first procedure utilizes the bosonic Josephson effect and controlled tunneling of atoms through the potential barrier, similar to laser light in an optical fiber coupler. The second one relies on the interference of the reflected and transmitted parts of the BEC wave function when impinging on the potential barrier, analogous to light impinging on a half-silvered mirror. Both schemes were implemented successfully, yielding an interferometric contrast of similar to 20% and 42% respectively. Building efficient matter-wave recombiners represents an important step towards the coherent manipulation of external quantum superposition states of BECs

Hyperglycemia and nocturnal systolic blood pressure are associatedwith left ventricular hypertrophy and diastolic dysfunction in hypertensive diabetic patients

BACKGROUND: The aim of this study was to determine if hypertensive type 2 diabetic patients, when compared to patients with essential hypertension have an increased left ventricular mass index (LVMI) and a worse diastolic function, and if this fact would be related to 24-h pressoric levels changes. METHODS: Ninety-one hypertensive patients with type 2 diabetes mellitus (DM) (group-1 [G1]), 59 essential hypertensive patients (group-2 [G2]) and 26 healthy controls (group-3 [G3]) were submitted to 24-h Ambulatory Blood Pressure Monitoring (ABPM) and echocardiography (ECHO) with Doppler. We calculated an average of fasting blood glucose (AFBG) values of G1 from the previous 4.2 years and a glycemic control index (GCI) (percentual of FBG above 200 mg/dl). RESULTS: G1 and G2 did not differ on average of diurnal systolic and diastolic BP. However, G1 presented worse diastolic function and a higher average of nocturnal systolic BP (NSBP) and LVMI (NSBP = 132 ± 18 vs 124 ± 14 mmHg; P < 0.05 and LVMI = 103 ± 27 vs 89 ± 17 g/m(2); P < 0.05, respectively). In G1, LVMI correlated with NSBP (r = 0.37; P < 0.001) and GCI (r = 0.29; P < 0.05) while NSBP correlated with GCI (r = 0.27; P < 0.05) and AFBG (r = 0.30; P < 0.01). When G1 was divided in tertiles according to NSBP, the subgroup with NSBP≥140 mmHg showed a higher risk of LVH. Diabetics with NSBP≥140 mmHg and AFBG>165 mg/dl showed an additional risk of LVH (P < 0.05; odds ratio = 11). In multivariate regression, both GCI and NSBP were independent predictors of LVMI in G1. CONCLUSION: This study suggests that hyperglycemia and higher NSBP levels should be responsible for an increased prevalence of LVH in hypertensive patients with Type 2 DM

Growth and nutrient uptake by potted foliage anthurium.

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On equations over sets of integers

Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition S+T=\makeset{m+n}{m \in S, \: n \in T} and with ultimately periodic constants is exactly the class of hyper-arithmetical sets. Equations using addition only can represent every hyper-arithmetical set under a simple encoding. All hyper-arithmetical sets can also be represented by equations over sets of natural numbers equipped with union, addition and subtraction S \dotminus T=\makeset{m-n}{m \in S, \: n \in T, \: m \geqslant n}. Testing whether a given system has a solution is $\Sigma^1_1$-complete for each model. These results, in particular, settle the expressive power of the most general types of language equations, as well as equations over subsets of free groups.Comment: 12 apges, 0 figure

Precision measurement of spin-dependent interaction strengths for spin-1 and spin-2 87Rb atoms

We report on precision measurements of spin-dependent interaction-strengths in the 87Rb spin-1 and spin-2 hyperfine ground states. Our method is based on the recent observation of coherence in the collisionally driven spin-dynamics of ultracold atom pairs trapped in optical lattices. Analysis of the Rabi-type oscillations between two spin states of an atom pair allows a direct determination of the coupling parameters in the interaction hamiltonian. We deduce differences in scattering lengths from our data that can directly be compared to theoretical predictions in order to test interatomic potentials. Our measurements agree with the predictions within 20%. The knowledge of these coupling parameters allows one to determine the nature of the magnetic ground state. Our data imply a ferromagnetic ground state for 87Rb in the f=1 manifold, in agreement with earlier experiments performed without the optical lattice. For 87Rb in the f=2 manifold the data points towards an antiferromagnetic ground state, however our error bars do not exclude a possible cyclic phase.Comment: 11 pages, 5 figure

Simple model of adsorption on external surface of carbon nanotubes: a new analytical approach basing on molecular simulation data

Nitrogen adsorption on carbon nanotubes is wide- ly studied because nitrogen adsorption isotherm measurement is a standard method applied for porosity characterization. A further reason is that carbon nanotubes are potential adsorbents for separation of nitrogen from oxygen in air. The study presented here describes the results of GCMC simulations of nitrogen (three site model) adsorption on single and multi walled closed nanotubes. The results obtained are described by a new adsorption isotherm model proposed in this study. The model can be treated as the tube analogue of the GAB isotherm taking into account the lateral adsorbate-adsorbate interactions. We show that the model describes the simulated data satisfactorily. Next this new approach is applied for a description of experimental data measured on different commercially available (and characterized using HRTEM) carbon nanotubes. We show that generally a quite good fit is observed and therefore it is suggested that the observed mechanism of adsorption in the studied materials is mainly determined by adsorption on tubes separated at large distances, so the tubes behave almost independently