von Neumann measurement-related matrices and the nullity condition for quantum correlation

We study von Neumann measurement-related matrices, and the nullity condition of quantum correlation. We investigate the properties of these matrices that are related to a von Neumann measurement. It is shown that these(m~2-1)×(m~2-1) matrices are idempotent, and have rank m-1. These properties give rise to necessary conditions for the nullity of quantum correlations in bipartite systems. Finally, as an example we discuss quantum correlation in Bell diagonal states.     

Spin effects and factorization in the Drell-Yan process

We discuss the idea that the nontrivial vacuum structure in QCD may induce transverse momentum and spin correlations of the initial state partons in Drell-Yan type reactions, i.e. in hadron-hadron collisions with production of a vector bosonV=γ ^*,Z,W ^±. Transverse momentum correlations are found to have practically no effect on observable quantities, but spin correlations have drastic consequences for the polarization density matrices of theV-bosons. We therefore propose measurements of theV polarization as a good test for the basic factorization hypothesis which, so far, has been assumed to be valid in numerous applications of the naive and QCD-improved parton model. We compare our ansatz for a spin correlation violating factorization with data from the NA 10 collaboration onγ ^* production inπ ^? N scattering. We find that the data give an indication of spin correlations of the partons in the initial state to be present.     

Robustness of Discrete Dynamics via Lyapunov Sequences

For a nonautonomous dynamics with discrete time defined by a sequence of matrices, we give a complete characterization of nonuniform exponential contractions and nonuniform exponential dichotomies in terms of Lyapunov sequences. We note that these include as very special cases uniform exponential contractions and uniform exponential dichotomies. Due to the central role played by these properties in a substantial part of the theory of dynamical systems, in particular in connection with the study of stable and unstable invariant manifolds, it is important to have available optimal characterizations that are more amenable to check whether a given dynamics has such a property. We also obtain inverse theorems that give explicitly Lyapunov sequences for a given contraction or dichotomy. As a nontrivial application, we establish the robustness under sufficiently small linear perturbations both of nonuniform exponential contractions and nonuniform exponential dichotomies. We emphasize that when compared to former work, our proof of the robustness property is much simpler. Partially supported by FCT through CAMGSD, Lisbon.     

Catalytic reactions in heavy-ion collisions

We discuss a new type of reactions of a ?-meson production on hyperons, ??Y ?? ?Y and antikaons -KN ?? ?Y. These reactions are not suppressed according to Okubo-Zweig-Iizuka rule and can be a new efficient source of ? mesons in a nucleus-nucleus collision. We discuss how these reactions can affect the centrality dependence and the rapidity distributions of the ? yield.     

Short- and long-range screening of optical phase singularities and C points

Screening of signed (charged) singularities-phase vortices in scalar fields, C points in vector fields, is discussed for paraxial optical fields with short- and long-range correlations. A circular region of radius R is assumed. Short-range screening is exemplified by a Gaussian field correlator, long-range screening by a J₀ Bessel function. The short-range screening length is obtained analytically; this is found to be in substantial agreement with recent experiments. For long-range screening, an accurate asymptotic formula suitable for quantitative comparison with data (numerical or laboratory) is derived for the variance of the net charge. A J₀ correlation function is not attainable in practice, but it is shown how to generate a pseudo-long-range optical field whose correlation function closely approximates this form; screening in such a field is well described by our theoretical results for J₀. The charge variance can be measured by three different methods: by counting positive and negative singularities inside the region of interest, by counting signed zero crossings on the perimeter of this region; or by measuring phase derivatives along the perimeter. For the first method, the charge variance is calculated by integration over the charge correlation function, for the second (third) by integration over the zero crossing (phase derivative) correlation function. It is proven explicitly that, as expected, all three calculations yield the same result. It is also shown analytically that for short-range screening the zero crossings can be counted along a straight line whose length is 2πR, but that for long-range screening this useful simplification no longer holds; for this case another formula is given that is suitable for data correction. The effects of boundary smoothing are discussed, and a class of generalized exponential smoothing functions is introduced. Analytical (numerical) results are given for the large R limit of the charge variance for the short (long) range case. Finally, it is shown that for realizable optical fields, both for the short and pseudo-long-range cases, for sufficiently small R the charge variance grows as R², whereas for sufficiently large R it grows as R.     

Swelling/deswelling of polyacrylamide gels in aqueous NaCl solution: Light scattering and macroscopic swelling study

Swelling kinetics of water-swollen polyacrylamide (PAAm) hydrogels (WSG) was investigated in various concentrations of aqueous NaCl by macroscopic swelling measurements. For lower concentration of NaCl, WSG showed exponential swelling whereas at higher concentration of NaCl it underwent deswelling at short times and exponential swelling at long times. From these studies, collective diffusion coefficient, D, of the polymer network and polymer?Csolvent interaction parameter, ??, were calculated and found to decrease with increase in [NaCl]. Collective diffusion coefficients measured from dynamic light scattering (DLS) and that obtained from macroscopic swelling measurements are found to agree well. Measured ensemble-averaged dynamic structure factor f(q,t) for WSG and salt-swollen gels (SSG) showed an initial decay followed by a plateau at long times and it can be described by harmonically bound Brownian particle (HBBP) model. Enhanced scattering intensity at low scattering angles using static light scattering (SLS) measurements revealed the presence of inhomogeneities in PAAm gels. The reasons for increased scattering intensity of SSG over WSG gel and the linear decrease of D with increase in NaCl concentration are explained.     

Quasi two bodye + e − annihilation

We present the helicity formalism fore ⁺ e^? annihilation into two-body resonance states, and show how to systematically extract the magnitudes and relative phases of the form factors present in the one-photon exchange approximation. This entails measurement of one-particle density matrices and certain polarization correlations in the final state. We discuss, as an example, the vector meson dominance expectations for annihilation into meson resonances and show how this model can be tested.     

Critical limit one-point correlations of monodromy fields on 321-1321-1321-1

Monodromy fields on ?² are a family of lattice fields in two dimensions which are a natural generalization of the two dimensional Ising field occurring in theC ^*-algebra approach to Statistical Mechanics. A criterion for the critical limit one point correlation of the monodromy field σ_a(M) at a ∈ ?², $$\mathop {\lim }\limits_{s \uparrow 1} \left\langle {\sigma _a (M)} \right\rangle ,$$ is deduced for matrices M ∈ GL(p,?) having non-negative eigenvalues. Using this criterion non-identity 2×2 matrices are found with finite critical limit one point correlation. The general set ofp×p matrices with finite critical limit one point correlations is also considered and a conjecture for the critical limitn point correlations postulated.     

The formation of correlated states and the increase in barrier transparency at a low particle energy in nonstationary systems with damping and fluctuations

We consider peculiarities in the formation of a coherent correlated state (CCS) of a particle in a periodically modulated harmonic oscillator with damping for various types of stochastic perturbation. It is shown that in the absence of stochastic perturbation, an optimal relation exists between the damping parameter (damping coefficient) and the modulation depth, for which the ??extrinsic?? characteristics of the oscillator (amplitudes of ??classical?? oscillation and the momentum of a particle) remain unchanged, while the correlation coefficient rapidly increases from |r| = 0 to |r|_max ?? 1; this corresponds to a completely correlated coherent state. Under nonoptimal conditions, the formation of the CCS with a simultaneous increase in is accompanied by damping or excitation of the oscillator. It is shown that for a certain relation between the damping coefficient and the modulation depth, the presence of a stochastic external force acting on the nonstationary oscillator does not prevent the formation of a CCS with |r|_max ?? 1. A fundamentally different effect is observed under a stochastic influence on the nonstationary frequency of the oscillator; this effect always limits the value of |r| at a level |r|_max < 1; a CCR cannot be formed with an unlimited increase in its intensity, and |r|_max ?? 0. The influence of the CCS formation on the averaged probability ??D?? of the tunnel effect (transparency of the potential barrier) is considered for a particle in an oscillator with damping both in the absence and in the presence of a stochastic force. It is shown using a specific example that complete clearing of the potential barrier and the increase in the barrier transparency from the initial value ??D _r=0?? = 10^?80 to ??D?? ?? 1 can occur over a comparatively short time interval in both these cases. These effects can be used to obtain highly efficient nuclear fusion at a low energy of interacting particles.     

Study of ferromagnetic correlations caused by impurities in nonmagnetic materials by the method of small-angle scattering of polarized neutrons

The possibility of the study of ferromagnetic correlations caused by d-metal impurities in nonmagnetic matrices is discussed. The polarization and magnetic-nuclear interference obtained by analyzing the small-angle scattering of polarized neutrons in a CuZn(20) alloy with Ni impurity (1 at %) are reported. It has been shown that Ni is clustered in the CuZn matrix with the characteristic correlation radius in the range 100 Å < R _c < 5000 Å depending on the thermal processing of the samples. The cross correlation function determining magnetic-nuclear interference is satisfactorily approximated by the exponential exp(?r/R _c), where r is the distance. It has been found that the nonmagnetic matrix CuZn(20) with an almost uniform distribution of 1% Ni impurity has metamagnetic properties in the field H ≈ 0.5 T at room temperature.     

Optimal weights decoding of M-ary suprathreshold stochastic resonance in stochastic pooling network

Suprathreshold stochastic resonance (SSR) is a noise enhancing signal processing phenomenon, occurring in a parallel array of nonlinear elements. In this paper, we investigate the optimal decoding scheme of SSR in stochastic pooling network with a quantization evolution of the output signal-to-quantization-noise ratio (SQNR) by studying the optimal weights and the optimal thresholds. Firstly, we introduce an effective method of weights decoding which makes the better SSR effects than the Wiener linear decoding and is defined as the optimal weights decoding. Moreover, in order to find the optimal thresholds, we select three common forms of thresholds in [0,1] interval the uniform thresholds, the random thresholds and the group thresholds. The result indicates that the group thresholds make a better SSR effect than uniform thresholds, but worse than the random thresholds. Therefore, the random thresholds are the optimal thresholds setting in the M-ary stochastic pooling network. Finally, we discuss the influences of number of elements N and threshold level M on SSR, and find that changing the number of the comparators N in stochastic pooling network is more easier to enhance the performance of SSR than changing the values of M. These works as a complement to the optimal quantification theory will be helpful for the study of optimal thresholds in stochastic pooling network.     

A new correlation based on artificial neural networks for predicting the natural gas compressibility factor

In this study a new correlation of natural gas compressibility factor based on theory of Mohammadikhah-Mohebbi-Abolghasemi??s equation of state (MMA EOS) is developed using an artificial neural network. In MMA EOS, the compressibility factor as a function of M-factor (BP/RT) is expressed. An artificial neural network (ANN) is designed in which the M-factor, reduced temperature, and reduced pressure are selected as input variables, whereas the natural gas compressibility factor is selected as output. Then, a new correlation based on the weights of ANN is obtained. Results of this correlation are compared with some other equations and experimental data. Proposed correlation for 597 data points has an average absolute deviation (AAD%) of 0.6% and a correlation coefficient (R ² value) of 0.9999.     

Dynamic structural correlations and Van Hove's correlation function for liquids

The stochastic model for liquids, developed previously and applied to the evaluation of static correlations, is extended to the evaluation of the dynamic pair correlation function. This extension can be achieved by a generalization of the width function W, characterizing the spread in the distribution of correlated local structures, from a piecewise linear function of r to a piecewise linear function in the (r, t) plane.     

Field theory of the random flux model

The random flux model (defined here as a model of lattice fermions hopping under the influence of maximally random link disorder) is analysed field theoretically. It is shown that the long range physics of the model is described by the supersymmetric version of a field theory that has been derived earlier in connection with lattice fermions subject to weak random hopping. More precisely, the field theory relevant for the behaviour of n-point correlation functions is of non-linear σ model type, where the group GL(n|n) is the global invariant manifold. It is argued that the model universally describes the long range physics of random phase fermions and provides further evidence in favour of the existence of delocalised states in the middle of the band in two dimensions. The same formalism is applied to the study of non-Abelian generalisations of the random flux model, i.e. N-component fermions whose hopping is mediated by random U(N) matrices. We discuss some physical applications of these models and argue that, for sufficiently large N, the existence of long range correlations in the band centre (equivalent to metallic behaviour in the Abelian case) can be safely deduced from the RG analysis of the model.     

HadronicW-decays at HERA

ep collisions at HERA will produce realW's with a cross section of almost 1 pb. We discuss to what extent the hadronic decays of theseW's will be visible above the QCD background. Using optimal cuts to enhance the hadronicW signal, a clearW peak should be visible after several years of running at HERA.     

Synchronization in scale free networks with degree correlation

In this paper we study a model of synchronization process on scale free networks with degree-degree correlations. This model was already studied on this kind of networks without correlations by Pastore y Piontti et al. [A.L. Pastore y Piontti, P.A. Macri, L.A. Braunstein, Phys. Rev. E 76 (2007) 046117]. Here, we study the effects of the degree-degree correlation on the behavior of the load fluctuations W_s in the steady state. We found that for assortative networks there exist a specific correlation where the system is optimally synchronized. In addition, we found that close to this optimal value the fluctuations does not depend on the system size and therefore the system becomes fully scalable. This result could be very important for some technological applications. On the other hand, far from the optimal correlation, W_s scales logarithmically with the system size.     

Towards a quantum field theory of primitive string fields

We denote generating functions of massless even higher-spin fields ??primitive string fields?? (PSF??s). In an introduction we present the necessary definitions and derive propagators and currents of these PDF??s on flat space. Their off-shell cubic interaction can be derived after all off-shell cubic interactions of triplets of higher-spin fields have become known. Then we discuss four-point functions of any quartet of PSF??s. In subsequent sections we exploit the fact that higher-spin field theories in AdS _d+1 are determined by AdS/CFT correspondence from universality classes of critical systems in d-dimensional flat spaces. The O(N) invariant sectors of the O(N) vector models for 1 ?? N ??? play for us the role of ??standard models??, for varying N, they contain, e.g., the Ising model for N = 1 and the spherical model for N = ??. A formula for the masses squared that break gauge symmetry for these O(N) classes is presented for d = 3. For the PSF on AdS space it is shown that it can be derived by lifting the PSF on flat space by a simple kernel which contains the sum over all spins. Finally we use an algorithm to derive all symmetric tensor higher-spin fields. They arise from monomials of scalar fields by derivation and selection of conformal (quasiprimary) fields. Typically one monomial produces a multiplet of spin s conformal higher-spin fields for all s ?? 4, they are distinguished by their anomalous dimensions (in CFT ₃) or by theirmass (in AdS ₄). We sum over these multiplets and the spins to obtain ??string type fields??, one for each such monomial.     

Relations betweenGL p,q (2)'s

Quantum groups have some peculiar properties is two dimensions. We formulate conditions sufficient for the product of two quantum matrices (with not necessarily the same values of deformation parameters) to be a quantum matrix again. This is then used to study the powers and exponential form of matrices fromGL _p,q (2), generalising this way properties ofGL _q (2)-matrices.     

Tripartite connection condition for a quantum graph vertex

We discuss formulations of boundary conditions in a quantum graph vertex and demonstrate that the so-called ST-form can be further reduced up to a form more effective in certain applications: In particular, in identifying the number of independent parameters for given ranks of two connection matrices, or in calculating the scattering matrix when both matrices are singular. The new form of boundary conditions, called the PQRS-form, also gives a natural scheme to design generalized low and high pass quantum filters.