Exact relations for correlation functions in the general Ising model

The exact relations for the correlation functions in the Ising model are obtained in the simplest form by the Green functions method for the arbitrary spin S and for the arbitrary coordination lattice number P.     

Time correlation functions of a one-dimensional infinite system

We investigate the time evolution of a simple one-dimensional system with an infinite number of particles. We calculate some time correlation functions and show that they behave asymptotically as 1/t.     

Thermodynamic limit of correlation functions in a system of gravitating fermions

We show that the correlation functions in a system of gravitating fermions converge as tempered distributions in the thermodynamic limit, if the system is not at the point of phase-transition. The densities converge to the density of the Thomas-Fermi-theory and are not correlated in the limit.     

Temperature and correlation functions in an isolated spin system

The probability distribution of electric field fluctuations in a stationary turbulent state of unstable ion-acoustic waves has been measured. For high instability levels the distribution function is found to be Gaussian. Deviations from the Gaussian shape are observed close to onset of the instability.     

Meson correlation functions in a QCD plasma

The temporal pseudoscalar meson correlation function in a QCD plasma is investigated in a range of temperatures exceeding T_c and yet of experimental interest. Only the flavour-singlet channel is considered and the imaginary time formalism is employed for the finite temperature calculations. The behaviour of the meson spectral function and of the temporal correlator is first studied in the HTL approximation, where one replaces the free thermal quark propagators with the HTL resummed ones. This procedure satisfactory describes the soft fermionic modes, but its application to the propagation of hard quarks is not reliable. An improved version of the so-called NLA scheme, which allows a better treatment of the hard fermionic modes, is then proposed. The impact of the improved NLA on the pseudoscalar temporal correlator is investigated.     

Simple relations for nuclear moments

Various relations for nuclearg-factors are extended, applied and discussed in view of recent experimental data. It is shown that the additivity relation can be used such that most of the corrections to theg-factor are accounted for. The isoscalar and isovector parts of theg-factor are studied in the mass regionA≦55 under the assumption of purej ⁿ configurations. For the isoscalar part the discrepancies with experiment are compatible with those for large shell-model calculations. Good results are obtained for the isovector part of theg-factor of ground states in mirror nuclei if both Gamow-Teller matrix elements, extracted from experimentalft values with an effective coupling constant ratio for Fermi and Gamow-Teller transitions, and assumptions on the seniority of the wave functions are used.     

Phase-modulus relations in cyclic wave functions

We derive reciprocal integral relations between phases and amplitude moduli for a class of wave functions that are cyclically varying in time. The relations imply that changes of a certain kind (e.g. not arising from the dynamic phase) obligate changes in the other. Numerical results indicate the approximate validity of the relationships for arbitrarily (non-cyclically) varying states in the adiabatic (slowly changing) limit.     

Gauge-invariant correlation functions for the Ising-gauge Ising-Higgs system in 2 dimensions

We use recent calculations of correlation functions of the 2-dimensional Ising model in the presence of a magnetic field to study the Z₂-gauge Z₂-Higgs system in 2 dimensions. We study both the correlation of two plaquettes and the gauge-invariant correlation of Higgs fields. From these we are able to discuss criteria for confinement in the presence of matter.     

Dipole correlation functions

Glarum's relation between permanent dipole correlation functions for an isolated sphere and a spherical region in a continuous medium is derived by molecular response theory and relation time development operators for the two cases.     

Triple correlation functions

New values for double mode-mode and triple flux molecular equilibrium correlations are presented. The relevance of these results for hydrodynamics is then discussed. It is found that the divergence of Burnett coefficients has only a formal meaning.     

Finite-temperature correlation functions

Lattice measurements of the Pisa group are analyzed numerically, and the parameters of correlation functions are extracted fromthe data—both below and above the deconfinement temperature T _c. The gluon condensate is found for six temperatures in the interval (0.956–1.131)T _c, and field distributions in the deconfined phase are obtained.     

Billiards correlation functions

We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and find results which are compatible with an exponential mixing hypothesis first put forward by Friedman and Martin (FM): they do not seem compatible with the stretched exponentials believed, in spite of FM and more recently of Chernov, to describe the mixing. The analysis leads to several byproducts: we obtain information about the normal diffusive nature of the motion and we consider the probability distribution of the number of collisions in timet _m (ast _m ), finding a strong dependence on some geometric characteristics of the locus of the billiard obstacles.This paper is dedicated to Philippe Choquard on his 65th birthday     

Mutual information functions versus correlation functions

This paper studies one application of mutual information to symbolic sequences: the mutual information functionM(d). This function is compared with the more frequently used correlation function(d). An exact relation betweenM(d) and(d) is derived for binary sequences. For sequences with more than two symbols, no such general relation exists; in particular,(d)=0 may or may not lead toM(d)=0. This linear, but not general, independence between symbols separated by a distance is studied for ternary sequences. Also included is the estimation of the finite-size effect on calculating mutual information. Finally, the concept of symbolic noise is discussed.     

Simple mass relations for bulk fermions

Relations between bulk mass parameters for fermions propagating in higher dimensions are studied in analogy with the empirical mass relation for charged leptons. Masses of three generation of four-dimensional charged leptons are achieved from the bulk mass parameters of the same-order values. We find that the observed pattern of charged-lepton mass spectrum is accommodated approximately in a set of simple relations for bulk and physical masses.     

Simple models of correlation in atoms

Brillouin's theorem, together with a power series expansion method, is used to explain the result (obtained by the numerical calculations of other workers) that the use of a Hartree-Fock 1s orbital in the correlation splitting approach to two-electron atoms is less satisfactory than the use of a screened hydrogenic orbital.     

Self-sustained oscillations in a closed side branch system

Self-sustained oscillations of the flow in a closed side branch system due to a coupling of vortex shedding with acoustical resonances are considered. The configuration consists of two closed side branches of same length placed opposite to each other along a main pipe. This is called a cross-junction. Numerical simulations, based on the Euler equations for two-dimensional inviscid and compressible flows, are performed. As the radiation into the main pipe is negligible at the resonance frequency, this acoustically closed system is a good test-case of such Euler numerical calculations. The numerical results are compared to acoustical measurements and flow visualization obtained in a previous study. Depending on the flow conditions, the predicted pulsation amplitudes are about 30-40% higher than the measured amplitudes. This is partially due to the absence of visco-thermal dissipation in the numerical model but also to the effect of wall vibrations in experiments. A simple analytical model is proposed for the prediction of the pulsation amplitudes. This model is based on Nelson's representation of the shear layer as a row of discrete vortices convected at constant velocity from the upstream edge towards the downstream edge. When the downstream edge is sharp, this results in a spurious interaction between the singularity of the vortices and of the edge flow. This artefact is partially compensated by suppressing the singularity of the acoustical flow at the edge, or when a junction with rounded edges, as found in engineering practice, is considered. In spite of its crudeness, the analytical model provides a fair prediction (within 30%) which makes it useful for engineering applications.