Long-range Jastrow correlations

We develop a promising many-body method to evaluate the equation of state for dense neutron matter and liquid helium. The ground state of the Fermi fluid is described by a conventional Jastrow ansatz. We admit the presence of short- and long-range correlations. Under this assumption we study the generating function which has been introduced by Wu and Feenberg. We employ a graphic formulation and develop the diagrammatic expansion of the generating function and the radial distribution function. If long-range correlations are assumed, the diagrams have singular parts. We give a proof that the total contribution of such diagrams to the generating function which contain two, three, and four correlation lines is of finite value. The same property is shown for a selected class of singular diagrams containing α correlation lines (α>4). To verify the cancellation phenomenon we introduce a two-body function which serves graphically as an insertion into selected singular diagrams. For the remaining classes of diagrams we need three-, four-, ?, n-body insertions. The result is cast into the form of a theorem. The cancellation rests on the exclusion principle and does not depend on the special shape of the correlation function. Finally, a generalized hypernetted-chain summation of diagrams which represent the radial distribution function is executed. The procedure includes exchange contributions and can be employed if short-and/or long-range correlations are present.     

Particle production in high-energy hadron-nucleus interactions

The pseudorapidity (η) distributions of fast particles (β>0.7) emitted in inelastic hadron interactions with carbon, copper and lead were measured for incoming energies from 50 to 150GeV at the CERN Super Proton Synchrotron. Their dependence on target mass (A) and projectile (h) obeys <v>-scaling as expected. Their energy dependence is in contrast with most model predictions.     

Multiplicities in highp t hadron-nucleus interactions

We present results obtained in π^? A (A=C, Cu, Pb) — collisions at 38 GeV/c. A single particle trigger selects events with one charged particle in the central region and large transverse momentum. The effect of this trigger on the multiplicities of all charged particles and of protons is shown.     

Long-range correlations in Boltzmann-Langevin model

The average phase-space density described by the Boltzmann-Langevin model can largely deviate from the one provided by the Boltzmann-Uhling-Uhlenbeck model, due to the non-linear evolution of density fluctuations. This aspect is investigated for long-wavelength, small density fluctuations in the framework of a memory incorporated Boltzmann-Langevin model. It is shown that the correlations associated with density fluctuations yield a collision term describing coupling between the collective vibrations and the single-particle degrees of freedom, which may play an important role in damping of collective motion in both the stable and unstable regions.     

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.     

Long-range interactions

A long-range potential is one whose range, the distance of effective influence, is unbounded or infinite. In this paper we show, using a definition of the range of a potential and certain other theoretical considerations, that the only long-range potential isV(r)=c/r, wherec is a constant.Supported in part by NASA Grant NSG-8035.     

The nuclear response in high-energy hadron-nucleus interactions

In an experiment at the CERN Super Proton Synchrotron (SPS) studying hadron-nucleus interactions, slow particles which are mainly knockout protons were measured with an electronic detector. Their dependence on the target mass, incoming energy, and projectile is shown. We discuss the use of the number of protons as a measure for the number of interactions of the projectile and conclude that the emitted protons measure the impact parameter of the reaction.     

Inclusive two-and three-particle rapidity correlations in high-energy hadron-nucleus collisions

Three-particle pseudorapidity correlations are investigated for relativistic secondaries from proton-nucleus interactions at 50, 67, 200 and 400 GeV/c and from pion-nucleus interactions at 50 and 200 GeV/c. The experimental data on two- and three-particle correlations are compared with quantitative predictions of current multiple scattering models of nuclear production. Within these models the influence of various factors on the magnitude of correlations is discussed and it is shown, in particular, that energy-momentum conservation plays an essential role at present accelerator energies.     

Multiplicity correlations of medium energy protons in hadron-nucleus collisions

Data on forward-backward multiplicity correlations of medium energy protons from hadron-nucleus collisions are presented and discussed.     

Long-range pair correlations in dilute gases

It is shown that there exist nonequilibrium pair correlations which are not described by the Boltzmann transport equation but which persist even in a dilute gas.     

Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).     

Multifractal thermodynamics of hadron-hadron and hadron-nucleus interactions

It is shown that the constant-specific-heat approximation is applicable to multifractal thermodynamics of hadron-hadron and hadron-nucleus interactions at high energies. Moreover, the constant specific heats calculated from experimental data on hadron-hadron and hadron-nucleus interactions have approximately the same value for both these types of multifractal multiproduction. Thus this parameter may turn out to be an universal characteristic of the hadron-hadron and hadron-nucleus interactions. Some relationship of this phenomenon to multifractal thermodynamics at the onset of chaos is briefly discussed. Received: 16 December 1997 / Revised version: 2 April 1998     

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.     

Long-range strain correlations in sheared colloidal glasses

Glasses behave as solids on experimental time scales due to their slow relaxation. Growing dynamic length scales due to cooperative motion of particles are believed to be central to this slow response. For quiescent glasses, however, the size of the cooperatively rearranging regions has never been observed to exceed a few particle diameters, and the observation of long-range correlations has remained elusive. Here, we provide direct experimental evidence of long-range correlations during the deformation of a dense colloidal glass. By imposing an external stress, we force structural rearrangements, and we identify long-range correlations in the fluctuations of microscopic strain and elucidate their scaling and spatial symmetry. The applied shear induces a transition from homogeneous to inhomogeneous flow at a critical shear rate, and we investigate the role of strain correlations in this transition.     

Long-range inverse two-spin correlations in one-dimensional Potts lattices

The inverse two-spin correlation function of a one-dimensional three-state Potts lattice with constant nearest-neighbor interactions in a uniform external field is derived exactly. It is shown that the external field induces long-range correlations. The inverse two-spin correlation function decays in a monotonie exponential fashion for a ferromagnetic lattice, while it decays in an oscillatory exponential fashion for an antiferromagnetic lattice. With no external field the inverse two-spin correlation function has a finite range equal to that of the interactions.     

Long-range correlations in the structure of fractal films

Hierarchically granulated films formed on a material subjected to the action of a high-temperature plasma have been microscopically studied. The statistical self-similarity of the structure of the surface from nanoscale to macroscale, as well as long-range correlations in the relief that are due to the statistically inhomogeneous structure of granularity, has been revealed.     

Long-range spatial correlations in a simple diffusion model

A simple anisotropic diffusion model, according to semiphenomenological arguments, exhibits long-ranged spatial correlations in uniform stationary states.