Decay of correlations in classical fluids with long-range forces

We show with simple arguments that, as a consequence of the Poisson equation, the correlations of a charged system at equilibrium decay faster than any inverse power, if they are integrable and monotonous at infinity. For all other longrange systems (with potential(x)b¦x¦^–s , ¦x¦ , 0v,s} 2), the decay is bounded below by an inverse power.Partially supported by the Swiss National Foundation for Scientific Research.     

Short range correlations in nuclei

Studying nucleon-nucleon (NN) correlated pairs will teach us a great deal about the high momentum part of the nuclear wave function, the short range part of the NN interaction, and the nature of cold dense nuclear matter. These correlations are similar in all nuclei, differing only in magnitude. High momentum nucleons, p > pfermi, all have a correlated partner with approximately equal and opposite momentum. At pair relative momenta of 300 < prel < 500 MeV/c, these correlated pairs are dominated by tensor correla-tions. This is shown by the dominance of pn over pp pairs at pair total momentum and by the parity of pn to pp pairs at large pair total momentum.     

Generalized Boltzmann equation for lattice gas automata

In this paper a theory is formulated that predicts velocity and spatial correlations between occupation numbers that occur in lattice gas automata violating semi-detailed balance. Starting from a coupled BBGKY hierarchy for then-particle distribution functions, cluster expansion techniques are used to derive approximate kinetic equations. In zeroth approximation the standard nonlnear Boltzmann equation is obtained; the next approximation yields the ring kinetic equation, similar to that for hard-sphere systems, describing the time evolution of pair correlations. The ring equation is solved to determine the (nonvanishing) pair correlation functions in equilibrium for two models that violate semidetailed balance. One is a model of interacting random walkers on a line, the other one is a two-dimensional fluid-type model on a triangular lattice. The numerical predictions agree very well with computer simulations.     

Short range correlations in nuclei

Studying nucleon-nucleon （NN） correlated pairs will teach us a great deal about the high momentum part of the nuclear wave function,the short range part of the NN interaction,and the nature of cold dense nuclear matter.These correlations are similar in all nuclei,differing only in magnitude.High momentum nucleons,p 〉p fermi,all have a correlated partner with approximately equal and opposite momentum.At pair relative momenta of 300 〈prel 〈500 MeV/c,these correlated pairs are dominated by tensor correlations.This is shown by the dominance of pn over pp pairs at pair total momentum and by the parity of pn to pp pairs at large pair total momentum.     

Critical point estimation and long-range behavior in the one-dimensional XY model using thermal quantum and total correlations

We investigate the thermal quantum and total correlations in the anisotropic XY spin chain in transverse field. While we adopt concurrence and geometric quantum discord to measure quantum correlations, we use measurement-induced non-locality and an alternative quantity defined in terms of Wigner–Yanase information to quantify total correlations. We show that the ability of these measures to estimate the critical point at finite temperature strongly depend on the anisotropy parameter of the Hamiltonian. We also identify a correlation measure which detects the factorized ground state in this model. Furthermore, we study the effect of temperature on long-range correlations.     

Sum rules for the one-component plasma with additional short-range forces

It is proved that, in the one-component plasma, with interactions including a non-Coulombic short-range part, the density derivative of the correlation functions _n (r ₁,,r _n) can be simply expressed as an integral of _n+1(r ₁,,r _n+1). This result is applied to prove the relation between the fourth moment of ₂ and the compressibility.     

Decay of correlations in spin systems

We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation.     

Multibin long-range correlations

A new method to study the long-range correlations in multiparticle production is developed. It is proposed to measure the joint factorial moments or cumulants of multiplicity distribution in several (more than two) bins. It is shown that this step dramatically increases the discriminative power of data.     

On the time evolution of the states of infinitely extended particles systems

We consider an infinite classical system of interacting particles in , . We study the time evolution of a particular class of nonequilibrium states. More precisely, the states we consider are Gibbs with respect to a Hamiltonian which differs from the Hamiltonian governing the motion by an external field (possibly not localized), satisfying certain conditions. It is proved that the time-evolved states satisfy superstable estimate and are described by correlation functions obeying the BBGKY hierarchy in a weak form.     

First-passage times in a critical stochastic model

Average first-passage times for a single-variable stochastic model with a critical fixed point at the origin are computed by exact enumeration. The numerical measurements show excellent agreement with analytical results. The scaling function approaches the predicted asymptotic dependence.     

Uniqueness for the BBGKY hierarchy for hard spheres in one dimension

We prove that the stationary BBGKY hierarchy for an infinite system of hard spheres in one dimension has a unique solution for all densities, within a symmetry class that pertains to either a fluid array or to a perfect crystalline array. The solution is shown to correspond to the uniform fluid, which is the only equilibrium state of the infinite system. The proof is subject to the recursion relation for the correlation functions found by Salsburg, Zwanzig, and Kirkwood, which we show exactly reduces the infinite hierarchy to a pair of coupled equations. A brief discussion is given of the existence of multiple solutions of an approximate BBGKY equation.     

Hydrodynamics and long range correlations

It is shown that the recently proposed method of studying the long-range correlations in multiparticle production can be effectively used to verify the hydrodynamic nature of the longitudinal expansion of the partonic system created in the collision. The case of ALICE detector is explicitly considered.     

Quantum correlations in optics

In many nonlinear optical problems, for example in down-conversion and four-wave mixing, the photons are generated in pairs. The strong correlation between the photons in a pair, characterized by either the correlations between operators corresponding to observables associated with individual photons, or the correlated state describing the two photons, may lead to various nonclassicalities. We discuss some of these nonclassical effects and their experimental demonstrations in nonlinear optical processes     

Long-range correlations in kinetic theory

It is shown that macroscopic correlations in a fluid are conserved for macroscopically long times. The equations of conservation can be written in a form independent of the density of the fluid and are therefore valid for a liquid as well as for a gas. The possibility of developing a kinetic theory of turbulence on the basis of these equations (along the lines of V. N. Zhigulev and of S. Tsugé) is indicated.The contents of this paper formed part of the Ph.D. thesis submitted by the author under the supervision of Prof. Harold Grad to the Department of Mathematics, New York University and issued as NYU-Courant Institute of Mathematical Sciences Technical Report MF-72, October 1973.     

Multiparticle azimuthal correlations

First observations of elliptic flow in Au-Au collisions at RHIC have been interpreted as evidence that the colliding system reaches thermal equilibrium. We discuss some of the arguments leading to this conclusion and show that a more accurate analysis is needed, which the standard flow analysis may not provide. We then present a new method of flow analysis, based on a systematic study of multiparticle azimuthal correlations. This method allows one to test quantitatively the collective behaviour of the interacting system. It has recently been applied by the STAR Collaboration at RHIC.     

Rigorous Derivation of the Cubic NLS in Dimension One

We derive rigorously the one-dimensional cubic nonlinear Schrödinger equation from a many-body quantum dynamics. The interaction potential is rescaled through a weak-coupling limit together with a short-range one. We start from a factorized initial state, and prove propagation of chaos with the usual two-step procedure: in the former step, convergence of the solution of the BBGKY hierarchy associated to the many-body quantum system to a solution of the BBGKY hierarchy obtained from the cubic NLS by factorization is proven; in the latter, we show the uniqueness for the solution of the infinite BBGKY hierarchy.     

Improvements in the clinical utility of calculated T2 images of the human brain

Magnetic Resonance Imaging (MRI) affords a considerable improvement in image contrast over other methods by virtue of the intrinsic NMR parameters spin density, T1, and T2. However, the clinical utility of routine quantification of these parameters is currently unknown. Calculated T2 images might afford additional disease specific information provided the calculation algorithm generates accurate T2 values. In this study, calculated T2 images of a MnCl2 phantom (spanning a T2 range of interest of 45.7 ms to 346.6 ms at 6 MHz) were generated utilizing a variety of calculation algorithms based upon a data set of 32 sequential spin-echo (SE) images. In general, when utilizing only the earliest sequential SE after the 90 degree pulse for the T2 calculation, the greater the number of SE used in the calculation algorithm, regardless of how they were averaged, the more accurate and less noisy was the calculated image. When only limited numbers of SE were used in the calculation algorithm, accuracy and noise varied with the choice of TE suggesting that there may be optimal timings for TE for a particular T2 range of interest. Forty-two calculated T2 head images of normal subjects, based upon data sets of 16 sequential SE, were evaluated for the T2 values of normal brain. These were compared to T2 images calculated via 7 different algorithms based upon 16 SE data sets from two patients with CNS pathology. An optimal algorithm was identified in which 16 SE Carr-Purcell-Meiboom-Gill (CPMG) were averaged into two images for the T2 calculation. With this algorithm, calculated images could be generated efficiently which were accurate and relatively noise free. The availability of such images maximized whatever disease specificity, and thus clinical utility, T2 information affords.     

Long-range correlations in two-dimensional spatio-temporal seismic fluctuations

We analysed the scaling behaviour of the two-dimensional (2-D) sequence (Δs, Δt) of the 1981–1998 southern California seismicity, where Δs is the distance between two consecutive earthquakes (jump) and Δt is their interevent interval. The 2-D seismic spatio-temporal fluctuations were investigated by means of the detrended fluctuation analysis (DFA), well-known methodology used to detect scaling behaviour in observational time series possibly affected by nonstationarities. The estimated scaling exponents α_DFA, larger than 0.5, indicate the presence of persistent long-range correlations in the 2-D sequence analysed. The variation of the scaling exponent with the increase of threshold magnitude shows a two-fold behaviour: in the range between 1.5 (the completeness magnitude of the catalog) and 3.0, the scaling exponent is quite constant and denoting a flicker-noise dynamics; while for magnitudes larger than 3.0 it decreases with the increase of magnitude, indicating a tendency toward a 2-D space–time Poissonian process for large events.