Factorial moments and short range correlation at relativistic energies

We present the results on cumulant moments obtained from horizontally and vertically averaged factorial moments for the shower particles, produced in³²S-emulsion at 200 A GeV,¹⁶O-emulsion at 200 A GeV,¹⁶O-emulsion at 60 A GeV,²⁸Si-emulsion at 14.5 A GeV and proton-emulsion at 800 GeV. Except the cumulants of order two, all other moments are consistent with zero within their statistical uncertainties. The strength of correlation length for each beam is higher than the previously observed values.     

Process with delta-correlated cumulants

In a recent paper¹) a differential equation was studied which involves a stochastic process having the property that all its cumulants are delta-correlated. It is here shown that such processes consist of a random sequence of delta functions with random coefficients. As a consequence the solutions of the differential equation are Markov processes, whose master equation can be constructed. From it closed equations for the successive moments may be obtained, and the auto-correlation is determined, in agreement with the results of reference 1. Some generalizations are given in Appendices B and C.     

Moment inequalities for the boltzmann equation and applications to spatially homogeneous problems

Some inequalities for the Boltzmann collision integral are proved. These inequalities can be considered as a generalization of the well-known Povzner inequality. The inequalities are used to obtain estimates of moments of the solution to the spatially homogeneous Boltzmann equation for a wide class of intermolecular forces. We obtain simple necessary and sufficient conditions (on the potential) for the uniform boundedness of all moments. For potentials with compact support the following statement is proved: if all moments of the initial distribution function are bounded by the corresponding moments of the MaxwellianA exp(−Bv ²), then all moments of the solution are bounded by the corresponding moments of the other MaxwellianA ₁ exp[−B ₁(t)v ²] for anyt > 0; moreoverB(t) = const for hard spheres. An estimate for a collision frequency is also obtained.     

Intermittency and correlations in hadronic Z^0 decays

A multidimensional study of local multiplicity fluctuations and multiparticle correlations of hadrons produced in Z decays is performed. The study is based on the data sample of more than events recorded with the OPAL detector at LEP. The fluctuations and correlations are analysed in terms of the normalized scaled factorial moments and cumulants up to the fifth order. The moments are observed to have intermittency-like behaviour, which is found to be more pronounced with increasing dimension. The large data sample allows for the first time a study of the factorial cumulants in annihilation. The analysis of the cumulants shows the existence of genuine multiparticle correlations with a strong intermittency rise up to higher orders. These correlations are found to be stronger in higher dimensions. The decomposition of the factorial moments into lower-order correlations shows that the dynamical fluctuations have important contributions from genuine many-particle correlations. The Monte Carlo models Jetset 7.4 and Herwig 5.9 are found to reproduce the trend of the measured moments and cumulants but they underestimate the magnitudes. The results are found to be consistent with QCD jet formation dynamics, although additional contributions from other mechanisms cannot be excluded. Received: 8 February 1999 / Published online: 8 September 1999     

Forward-backward multiplicity distributions in the Peřina-McGill scheme and analysis ine + e − collisions

A forward-backward multiplicity correlation is considered by the use of the Pe?ina-McGill formula. We obtain analytic formulae for conditional cumulants of the backward multiplicity and a conditional backward multiplicity distribution at a given forward multiplicity. The multiplicity distribution and the conditional mean multiplicity observed at \(\sqrt s = 29\) in HRS ine ⁺ e ^? collisions are analysed. We predict the conditional moments and the conditional backward multiplicity distribution. Those should be compared with the future analyses in HRS.     

Inseparability criteria for continuous bipartite quantum states

We provide necessary and sufficient conditions for the partial transposition of bipartite harmonic quantum states to be nonnegative. The conditions are formulated as an infinite series of inequalities for the moments of the state under study. The violation of any inequality of this series is a sufficient condition for entanglement. Previously known entanglement conditions are shown to be special cases of our approach.     

Combinatorics of Bi-Freeness with Amalgamation

In this paper, we develop the theory of bi-freeness in an amalgamated setting. We construct the operator-valued bi-free cumulant functions, and show that the vanishing of mixed cumulants is necessary and sufficient for bi-free independence with amalgamation. Further, we develop a multiplicative convolution for operator-valued random variables and explore ways to construct bi-free pairs of B-faces.     

Bohmian and quantum phase space distribution expansions and approximations

Dias and Patra derived an expansion of the Wigner distribution and related it to the de Broglie–Bohm model. We show that the coefficients of the expansion are related to the conditional central moments and cumulants of the Wigner distribution. The even order cumulants depend only on the amplitude of the wave function and the odd order cumulants depend only on the phase. In addition, we give a different expansion of the Wigner distribution from which their expansion can be derived as a special case. Our expansion allows for different approximations for higher order terms. We also give expansions for the momentum representation. We show how the results are applicable to pulse propagation in a dispersive medium.     

Factorial cumulant moments and correlation integrals in pp collisions at 400 GeV/c

The pseudorapidity distribution of charged particles produced in pp collisions at 400 GeV/c was measured by using LEBC films offered by CERN NA27 collaboration. The scaled factorial cumulant moments have been calculated. The results show that the second order cumulants have positive values, while the cumulants of higher order are consistent with zero except for the situation ofn _ch ≥ 4 events, where the third-order cumulants have positive values beyond the statistical uncertainties. It means that the observed increase of the higherorder factorial momentsF _q is almost due to the dynamical two-particle correlation in pp collisions at 400 GeV/c. The cumulant moments also have been calculated by star correlation integrals. It significantly reduced the statistical errors, especially for higher order cumulants. From Monte Carlo events with the same single particle spectrum and no correlations, we observed that for broad mixed-multiplicity distributions, a significant part ofK ₂ is coming from the single-particle fluctuation due to the fluctuating multiplicity.     

How to Prove Dynamical Localization

Let H be a self-adjoint operator on l ²(Z ^d ) or L ²(R ^d ) with pure point spectrum on some interval I. We establish general necessary and sufficient conditions for dynamical localization for a given vector and on the interval of energies I. The sufficient conditions we obtain improve the existing ones such as SULE or WULE and can be useful in applications. Received: 16 November 2000 / Accepted: 14 February 2001     

Factorial moments,cumulants and correlation integrals in π+ p andK + p interactions at 250 GeV/c

A selected sample of 59200 π⁺ p andK ⁺ p nonsingle-diffrative interactions at \(\sqrt s \) =22 GeV is used to investigate one, two- and three-dimensional factorial moments, factorial cumulant moments, as well as correlation integrals. The rise of factorial moments and cumulants with decreasing phase-space volume is stronger when evaluated in three than in lower dimensions. Ratios of slopes are easier to obtain than the slopes themselves. Contrary to earlier findings, they turn out to depend on the dimension. The order dependence of the averaged ratios is better described by a Lévy stable law solution with μ=1.6 than by Gaussian approximation of the α-model (μ=2) or a second order phase transition (μ=0), but values μ>2 inconsistent with Lévy-type fluctuations are reached in a three-dimensional analysis. The multiparticle contributions to the factorial moments are calculated by means of factorial cumulant moments. A particular improvement of the method is that of correlation (or density) integrals. It leads to the conclusion that Bose-Einstein interference plays an important role in the intermittency effect, but indication is found for an interpretation alternative to the conventional view of Bose-Einstein correlations.     

Event-by-event efficiency fluctuations and efficiency correction for cumulants of superposed multiplicity distributions in relativistic heavy-ion collision experiments

We performed systematic studies on the effects of event-by-event efficiency fluctuations on efficiency correction for cumulant analysis in relativistic heavy-ion collision experiments. Experimentally, particle efficiencies of events measured under different experimental conditions should be different. For fluctuation measurements, the final event-by-event multiplicity distributions should be the superposed distributions of various type of events measured under different conditions. We demonstrate efficiency fluctuation effects using numerical simulation, in which we construct an event ensemble consisting of events with two different efficiencies. By using the mean particle efficiencies, we find that the efficiency corrected cumulants show large deviations from the original inputs when the discrepancy between the two efficiencies is large. We further studied the effects of efficiency fluctuations for the cumulants of net-proton distributions by implementing the UrQMD events of Au+Au collisions at sNN~(1/2) = 7.7 GeV in a realistic STAR detector acceptance. We consider the unequal efficiency in two sides of the Time Projection Chamber(TPC), multiplicity dependent efficiency, and the event-by-event variations of the collision vertex position along the longitudinal direction(V_z). When the efficiencies fluctuate dramatically within the studied event sample,the effects of efficiency fluctuations have significant impacts on the efficiency corrections of cumulants with the mean efficiencies. We find that this effect can be effectively suppressed by binning the entire event ensemble into various sub-event samples, in which the efficiency variations are relatively small. The final efficiency corrected cumulants can be calculated from the weighted average of the corrected factorial moments of the sub-event samples with the mean efficiencies.     

Full counting statistics of phonon transport in disordered systems

The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calculate up to the 8-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method. The benchmark shows that the FCS-CPA method achieves 20 times more speedup ratio. Collective features of phonon current cumulants are also revealed.     

Independent particle Schrödinger fluid: Moments of inertia

The philosophy of the single particle Schrödinger fluid, especially as regards the velocity fields which find such a natural role therein, is applied to the study of the moments of inertia of independent fermion system. It is shown that three simplified systems exhibit the rigid-body rotational velocity field in the limit of large A, and that the leading deviations, both on the average and fluctuating, from this large-A limit can be described analytically, and verified numerically. For a single particle in a Hill-Wheeler box the moments are studied numerically, and their large fluctuations identified with the specific energy level degeneracies of its parallelepiped shape. The full assemblage of these new and old results is addressed to the question of the necessary and sufficient condition that the moment has the rigid value. Counter examples are utilized to reject some conditions, and the conjecture is argued that unconstrained shape equilibrium might be the necessary and sufficient condition. The spheroidal square-well problem is identified as a promising test case.     

Random Matrix Theory and ζ(1/2+it)

We study the characteristic polynomials Z(U, θ) of matrices U in the Circular Unitary Ensemble (CUE) of Random Matrix Theory. Exact expressions for any matrix size N are derived for the moments of |Z| and Z/Z ^*, and from these we obtain the asymptotics of the value distributions and cumulants of the real and imaginary parts of log Z as N→∞. In the limit, we show that these two distributions are independent and Gaussian. Costin and Lebowitz [15] previously found the Gaussian limit distribution for Im log Z using a different approach, and our result for the cumulants proves a conjecture made by them in this case. We also calculate the leading order N→∞ asymptotics of the moments of |Z| and Z/Z ^*. These CUE results are then compared with what is known about the Riemann zeta function ζ (s) on its critical line Re s= 1/2, assuming the Riemann hypothesis. Equating the mean density of the non-trivial zeros of the zeta function at a height T up the critical line with the mean density of the matrix eigenvalues gives a connection between N and T. Invoking this connection, our CUE results coincide with a theorem of Selberg for the value distribution of log ζ(1/2+iT) in the limit T→∞. They are also in close agreement with numerical data computed by Odlyzko [29] for large but finite T. This leads us to a conjecture for the moments of |ζ(1/2+it) |. Finally, we generalize our random matrix results to the Circular Orthogonal (COE) and Circular Symplectic (CSE) Ensembles. Received: 20 December 1999 / Accepted: 24 March 2000     

On the implementability of non*Bogoliubov automorphisms of CAR algebras on fock spaces

We give necessary and sufficient conditions for the implementability of non^*Bogoliubov automorphisms of CAR algebras on Fock spaces. As an application, we show that certain (projective) representations of loop groups cannot be extended to bounded representations of their complexified groups.     

On tangential properties of the Gutt 1-product

We establish necessary and sufficient conditions on a Lie algebra g, under which the Gutt 1-product on g¹ is tangential to a given coadjoint orbit.     

Invariant mass dependence of particle correlations in π+ p andK + p interactions at 250 GeV/c

We study two- and three-particle correlations as a function of invariant mass. Using data on π⁺ p andK ⁺ p collisions at 250 GeV/c, we compare correlation functions and normalised factorial cumulants for various charge combinations. Strong positive correlations are observed only at small invariant masses. The normalised cumulants for “exotic” [(??), (++)] and “nonexotic” pairs (+?) and triplets decrease in power-like fashion with increasing invariant mass. The mass dependence is not incompatible with the power-law behaviour as expected in a Dual Mueller-Regge framework. Comparison with FRITIOF reveals strong disagreements, which are due to too large production rates of resonances, such as ρ⁰ and η, and the absence of a Bose-Einstein low-mass enhancement in JETSET.

     

MOMENT EXPANSIONS OF PROTON DIPOLAR SPINNING-SIDEBAND INTENSITIES IN A 1H MAS NMR SPECTRUM

对于包含分子和分子基团绕至少一个轴高速运动的固体体系，本文推导出其质子核磁共振谱的偶极魔角旋转边带强度的理论计算表达式，建立了用其静态粉末谱的矩的展开的计算方法，计算出旋转边带强度按三十阶矩展开的系数，它可以处理包含高达十五阶边带的谱.     

The quasi-multiplication on rings and algebras

On a ring or an algebra we introduce the quasi-multiplication a b = ab + a + b, taking into account the multiplication and addition simultaneously. An example shows that this quasi-multiplication has remarkable and fundamental properties.