Extremal spacings between eigenphases of random unitary matrices and their tensor products

Extremal spacings between eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N = 4. We study ensembles of tensor product of k random unitary matrices of size n which describe independent evolution of a composite quantum system consisting of k subsystems. In the asymptotic case, as the total dimension N = n^k becomes large, the nearest neighbor distribution P(s) becomes Poissonian, but statistics of extreme spacings P(s_min) and P(s_max) reveal certain deviations from the Poissonian behavior

Barycentric measure of quantum entanglement

Majorana representation of quantum states by a constellation of n 'stars' (points on the sphere) can be used to describe any pure state of a simple system of dimension n+1 or a permutation symmetric pure state of a composite system consisting of n qubits. We analyze the variance of the distribution of the stars, which can serve as a measure of the degree of non-coherence for simple systems, or an entanglement measure for composed systems. Dynamics of the Majorana points induced by a unitary dynamics of the pure state is investigated.Comment: 11 pages, 13 figure

Birkhoff's polytope and unistochastic matrices, N=3 and N=4

The set of bistochastic or doubly stochastic N by N matrices form a convex set called Birkhoff's polytope, that we describe in some detail. Our problem is to characterize the set of unistochastic matrices as a subset of Birkhoff's polytope. For N=3 we present fairly complete results. For N=4 partial results are obtained. An interesting difference between the two cases is that there is a ball of unistochastic matrices around the van der Waerden matrix for N=3, while this is not the case for N=4.Comment: 30 pages, 4 figure

Geometry of entangled states

Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem and characterize the set of effectively different states (which cannot be related by local transformations). Thus we generalize earlier results obtained for the simplest 2 x 2 system, which lead to a stratification of the 6D set of N=4 pure states. We define the concept of absolutely separable states, for which all globally equivalent states are separable.Comment: 16 latex pages, 4 figures in epsf, minor corrections, references updated, to appear in Phys. Rev.

Family of Zeilinger-Horne-Greenberger "W" states lead to stronger nonclassicality than family of Greenberger-Horne-Zeilinger "GHZ" states

The N-qubit states of the W class, for N>10, lead to more robust (against noise admixture) violations of local realism, than the GHZ states. These violations are most pronounced for correlations for a pair of qubits, conditioned on specific measurement results for the remaining (N-2) qubits. The considerations provide us with a qualitative difference between the W state and GHZ state in the situation when they are separately sent via depolarizing channels. For sufficiently high amount of noise in the depolarizing channel, the GHZ states cannot produce a distillable state between two qubits, whereas the W states can still produce a distillable state in a similar situation.Comment: v3: 7 pages, 2 figures, REVTeX4; v2: result on comparative yield of singlets added, 1 new figur

Numerical and experimental analysis of the velocity field of air flowing through swirl diffusers

The air swirl diffusers are popular for the ceiling level air supply system and have been widely used for Indoor Air Quality. They are nowadays one of the most popular diffusers commonly used in airconditioning systems [1, 2]. The swirl diffusers are intended to use in low- and medium-pressure ventilation systems. They allow for obtaining the swirl airflow and are especially recommended to use in spaces with the height from 3m up to 12m, where heating and cooling is performed by the ventilation system and where the exact setting of supply air velocity is important [3-6]. In the case of swirl diffusers,fluid flow is usually significantly influenced by the characteristics of different diffuser designs. In the ventilation system design phase, a typically focus on ventilation effectiveness and takes into account a large number of parameter. However, the discrepancy between design and practice are often experienced mainly because operating conditions don’t correspond to the designing conditions [7-9]. Inthis work, the airflow of swirl diffuser has been studied using Particle Image Velocimetry (PIV) method to analyse the mean airflow and geometry influence on the results. The paper presents a comparison of the results of velocity field measurements using the PIV method and the results obtained by means ofnumerical analysis CFD. Based on the analysis the velocity flow field was evaluated and the range of effective operation of the diffuser have been determined [10]

Method of Air Temperature Forecast in Mechanized Longwall Workings in the Conditions of Vietnamese Mines

In the most recent years, the Vietnam National Coal - Mineral Industries Holding Corporation Limited (VINACOMIN) has been dynamically developing mechanization technologies in underground coal mines. The climatic conditions of Vietnam, as well as increasing the depth of the coal seams and the production capacity, contribute to an air temperature increasing in mining excavations. The article presents statistical equations enabling air temperature forecasting at the outlet of mechanized longwall workings. The results of numerical calculations, obtained from the solutions of the adopted mathematical descriptions, were compared with the measurement results and the statistical significance of the obtained deviations was determined. The performed analysis allowed to assess the practical usefulness of the adopted model for the air temperature forecasting in the workings of mechanized underground mines in Vietnam. The presented method can be used as a tool for mining services in the fight against the climate threat in underground excavations

Dobór i obliczenia rozwiązań chłodzenia powietrza w podziemnych kopalniach węgla w Wietnamie

Currently, Vietnamese underground mines have been exploited down to -500 m and, in the near future, they will be exploited deeper. The exploitation of coal of seams has an negative impact on a workers environment. The increase in the depth of coal seam exploitation causes is the increase of adverse microclimate factors such as temperature, moisture, heat radiation. According to the current Viet¬namese laws, coal deposits can be mined in a condition when air temperature does not exceed 30oC, although this rule is not always observed, especially during summer. The article show how reducing the adverse impact of climate factors in the mines and calculating the parameters which reduce the temperature on an example in one of underground coal mines in Vietnam.Obecnie wietnamskie kopalnie podziemne zostały wyeksploatowane do -500 m, w najbliższej przyszłości będą eksploatowane głębiej. Eks¬ploatacja ma negatywny wpływ na środowisko. Działalność eksploatacji w wyrobiskach powoduje wzrost niekorzystnych czynników mi-kroklimatycznych, takich jak temperatura, wilgotność, promieniowanie cieplne. Zgodnie z obowiązującym wietnamskim prawem, złoża węgla mogą być eksploatowane w warunkach, gdy temperatura powietrza nie przekracza 30°C, chociaż nie zawsze jest to przestrzegane, zwłaszcza latem. W artykule przedstawiono rozwiązanie ograniczania niekorzystnego wpływu czynników klimatycznych w kopalniach oraz obliczenie parametrów obniżających temperaturę powietrza na przykładzie podziemnych kopalń węgla w Wietnamie