Note on the Paper “Gibbs vs. Shannon Entropies” by Richard L. Liboff

In addition to the comparison of the Gibbs negentropy η_G = ∫ Π ln Π to the Shannon negentropy ηs = ∑ E_iΠ_i ln(E_iΠ_i), discussed in the cited paper, a comparison of the former to η_s′=η_s?∑E _i lnE _i the decrease in uncertainty, is of general interest from an information-theoretic standpoint. It is shown that η_G and η_s′ are similar in the situation in question. The additivity properties of η_G are briefly discussed.     

Measurement of the Baryon-exchange reactions K−p→Λη, K−p→Λπ0 at 6 GeV/c and the value of the ηNN coupling constant

In order to determine the ηNN coupling constant we have measured the two reactions K^?p→Λη and K^?p→Λπ⁰ with a magnetic wire chamber spectrometer which contained a gamma counter for the γγ decays of π⁰ and η. The Λ polarization and the differential cross sections are given. The latter have quite different u dependences. Their ratio is interpreted, in terms of a nucleon-Regge exchange model, as the effect of a small ηNN coupling constant for which we obtain G_ηNN² = G_πNN² · (0.26 ± 0.10) as allowed by SU(3). The large value given by Heisenberg's non-linear field theory, G_ηNN² = G_πNN² · 0.9, is excluded by this measurement if the characteristic u dependence of the Λπ⁰ channel is attributed to N_α Regge exchange.     

J/ψ+η′ Production ine + e −-annihilation: A perturbative QCD calculation

The cross section for the reactione ⁺ e ^?→³S₁+¹S₀ is calculated in the framework of perturbative QCD, using the nonrelativistic approximation for the³S₁ and¹S₀ bound states. The model is applied toJ/Ψ plus η,η,η′, andl production. We find extremely small rates in contrast to previous estimates based on vector meson dominance and discuss possible reasons for this difference.     

Study of the reaction π− p→η′η′n

The reaction π^? p→η′η′n has been studied atp _π=37 GeV/c. Total of 14 events of this reaction have been selected. It has been shown that in the effective mass spectrum of the η′η′ system the events are concentrated mainly near the reaction threshold, which might be caused by the decayX(1910)→η′η′. The reaction cross-section has been evaluated: σ(π^? p→η′η′n)=110±40 nb.     

Two schemes ofη−η′-mixing

Proceeding from the expansion of composite operators in interpolating hadronic fields, the width of the decays η(η′)→γγ andJ/ψ→η(η′)γ have been calculated. Two mechanisms of pseudoscalar field mixing (“mass-mixing” and “current-mixing”) are considered. In the given schemes, the values of η?η′-mixing angle θ _p are, respectively, (?15.0±1.8)^o and (?19.7±2.2)^o.     

Generalizing some properties of short range classical solutions to Yang-Mills theory

We extend a theorem which states that for classical solutions of Yang-Mills theory, the field G_μν has to decrease at least as fast as the source S_μ at spatial infinity, provided G_μν decreases exponentially [G_μν ～ exp(?Mr)]. This generalization encompasses all decreases G_μν ～ exp(?Mr^η) with η > 0, r→∞. This is done by assuming an integral representation for A_μ, the vector potential, and imposing some regularity conditions on A_μ, valid as r→∞.     

Spectral representation for singlet and triplet green's functions

Spectral representations of special Green functions are given explicitly. We consider the density correlation functionG ₂(x ₁ η ₁ x ₂ η ₂,x ₁ ⁺ η ₁ x ₂ ⁺ η′₂) and the functionG ₂(x ₁ η ₁ x ₁ ^? η₂,x ₂ η ₁ ^′ x ₂ ^? η ₂ ^′ Coupling the field operators Ψ^? (x, η), Ψ(x, η) to singlet and triplet operatorsA _{SMs TT3} (x), we obtain spectral representations for theseG-functions. The formulae derived may be of use when studying the system of equations for the Green functions, which describe many particle systems from a microscopic point of view.     

Search for CP-violation in Ko→3πo decay

Using the 180 liter ITEP liquid xenon bubble chamber the time distribution of 22 K^o → 3π^o decays has been studied. For the ratio η_ooo of amplitudes K_S → 3π^o and K_L → 3π^o decays we found Reη_ooo = ?0.04 ± 0.45 and Imη_ooo = 0.45 ± _0.65^0.50. Assuming CPT invariance we obtained |η_ooo|² < 1.2 and Γ(K_S → 3π^o)/ Γ(K_S) ? 4.3 × 10^?4 at 90% confidence level.     

Inclusive ηp and ηn charged-current neutrino reactions below 6 GeV

Results are presented of a study of inclusive ηp and ηn interactions from threshold to 6 GeV. The data show a rapid approach to the distributions expected in the naive quark-parton model. The charged-current η deuteron total cross section is fit by the expression σ_T(ηd) = (0.76 ± 0.03) × 10^?38E_η cm² per GeV per nucleon. For E_η > 1.5 GeV, we measure σ_T(ηn)/σ_T(ηp) = (2.02 ± 0.23). The distributions in the scaling variables x and y are given and discussed.     

The reaction π−p → ηn up to pη1 = 450 MeV/c: experimental results and partial-wave analysis

An accurate measurement of $\text{d}\text{σ}\text{d}\text{Ω}\text{(π}{}^{\mathrm{?}}\text{p}\text{→ η}\text{n}\text{)}$ at 1531 MeV total energy (expanded) up to l = 4 Legendre polynomials) requires reconsideration of previous angular distribution fits which were expanded only up to l = 2 and of subsequent partial-wave analysis. An energy-dependent partial-wave analysis has been performed here for $\text{p}{}_{\mathrm{\eta }}{}^1$ up to 450 MeV/c. In addition to the well-known S₁₁ (1520 MeV) resonance, either the P₁₁ (1532 MeV) or the P₁₃ (1530 MeV) resonance is found to be strongly coupled to the η-n channel. In both cases, the P₁₁ (1729 MeV) resonance is needed as is the weakly coupled D₁₃ (1525 MeV) resonance. The decay states in the ηn channelare compared to the SU(3) and SU(6)_W predictions.     

Space and wavelength dependence of speckle intensity

A unified, analysis is presented for the spatial and the spectral sensitivity of speckle (the rapid spatial variations which occur in an image when illumination of narrow spectral width is used) in a space-invariant linear system. In prior work considering speckle size, others have shown that its spatial variation is functionally dependent primarily on the autocorrelation function of the system's impulse response, but effects of varying the wavelength were largely ignored. In the present paper we treat the general problem in which a diffuse object, illuminated by a collimated, monochromatic beam, is imaged by a system whose amplitude impulse response isz(x, η), wherex and η are space and normalized (temporal) frequency coordinates, respectively. An expression is derived for the multidimensional autocorrelation functionR _u (Δx,η ₁,η ₂) of the intensityu(x,η) in the image plane. Functionally, it depends upon a convolution of the system autocorrelation functionR _u (Δx,η ₁,η ₂) with the characteristic function of the distribution function for heights, which is used to model the input object's surface. Examples are presented; and, it is shown that one can infer valuable information about the variation of heights for points on the surface of the input diffuse object, which are separated by much less than the classical resolution limit.     

Classical and quantum percolation phenomena and controlling them in eutectic semiconductor-superconductor compositions

Experimental data on the conduction of heterogeneous systems have been traditionally interpreted in the context of the theory of percolation phenomena taking into account the relative threshold volume fraction η_C ≈ 0.16) of the high-conductivity phase. This work is concerned with the conduction of eutectic compositions semiconductor-normal metal at T > T _c (the classical limit) and semiconductor-superconductor at T < T _c (the quantum limit) obtained at various material growth rates; these materials contain metal particles as oriented whiskers in semiconducting matrices. The paper presents spatial and energy models of discrete, finite, and infinite clusters that well explain classical and quantum percolation conductivities. Depending on the growth rate of eutectic compositions, their classical and quantum conductivities can manifest themselves at arbitrary percolation thresholds η_p (0 < η_p ≤ η_c). It is shown that the density of whiskers, the distances between them, their diameters, and the critical supercurrent density per whisker can be controlled by varying the rate of composition growth.     

Neutral decays ofη′(958)

The partial widths of the η′(958) decays into 2γ, ωγ, 3π⁰ andηπ⁰π⁰ have been measured with the GAMS-2000 spectrometer at the 70 GeV IHEP accelerator. Upper limits for the η′ decays into 3γ, π⁰γγ, 2π⁰ and 4π⁰ have also been obtained. The slope of a linear matrix element for theG-parity violating decayη′→3π⁰ has been determined.     

The isobar model of the γN → ηN processes in the energy range from the threshold to 1200 MeV

The isobar model of the γN → γN processes is constructed on the basis of the precision measurements of the cross section for the γp → ηp process near the threshold in Mainz (Germany) and the sensational results of recent measurements of the Σ beam asymmetry and dσ/dΩ for this process in Grenoble (France). The model involves six nucleon resonances (MeV): S ₁₁(1535), S ₁₁(1650), P ₁₁(1440), P ₁₃(1720), D ₁₃(1520), and F ₁₅(1680). The properties of these resonances are discussed. The P ₁₃(1720) and F ₁₅(1680) resonances are responsible for large positive values of the Σ beam asymmetry for the γp → ηp reaction at small angles. The contribution of the S ₁₁(1650) resonance must be taken into account in addition to the contribution of the S ₁₁(1535) resonance in order to describe the experimental dependence of the total cross section on the photon energy. The values characterizing the γn → ηn reaction are calculated on the basis of the available data on the amplitudes of electromagnetic excitation of these resonances on protons and neutrons.     

Volume viscosity and structure of n-propanol by ultrasonics

The adiabatic volume viscosities η_v and η′_v have been evaluated in n-propanol along with X₂ (the molefraction of molecules arranged in pairs with antiparallel dipole moments), using experimental ultrasonic absorption data in the temperature range 10°C to 80°C. Both η_v and η′_v decrease nonlinearly with temperature and the ratio η′_v/η_v is found to be nearly unity at all temperatures.     

A disordered ising model with internal degrees of freedom

A solvable Ising-system withnn-interactions as a basic system is considered. This system is assumed to undergo a phase transition so that the thermal quantityq=Σ _i> ₀ ² /N, which is not necessarily the order parameter of the basic system, is different from zero (q≠0) forT _c. The whole system consists of the basis {S _i} and an equal number of additional spins η _i which are coupled linearly with the basic spinsS _i through an exchange constantJ _i which is distributed at random. The pairs of spinsS _i ?η _i can be interpreted as clusters with an internal degree of freedom. The specific heat Δc and the susceptibility Δ_χ of the internal degree of freedom can be separated exactly and show typical spin glass properties: the specific heat Δc is an analytic function over the whole temperature range and the susceptibility Δ_χ shows a cusp at the transition temperatureT _c of the basic system.     

Measurement of light scalar mesons in many-body decays in the PHENIX experiment at the Relativistic Heavy-Ion Collider

The unique design of the PHENIX detector at the Relativistic Heavy-Ion Collider allows one to detect neutral and charged particles produced in high-energy collisions of heavy ions. This circumstance made it possible to measure many-particle decays of light mesons, such as K _S ⁰ →π⁰π⁰, η→π⁰π^?π⁺, and η→γγ in p + p, d + Au and Au + Au collisions at the energy \(\sqrt {S_{NN} }\) = 200 GeV. The latest results of measuring the differential production cross sections, ratios of particle yields (K _S ⁰ /π⁰ and η/π⁰), and the nuclear modification factors (\(R_{dA}^{K_S }\), R _dA ^η , R _AA ^η ) in a wide range of transverse momenta (from 2 to 12 GeV s^?1) are reported.     

Measurement of the boundary frequency of the inertial interval of capillary wave turbulence at the surface of liquid hydrogen

The boundary frequency was experimentally measured for the upper edge of an inertial interval corresponding to the Kolmogorov spectrum for energy distribution over the oscillation frequencies at the surface of liquid hydrogen. It is shown that the dependence of boundary frequency ω_b on the wave amplitude η_p at the pump frequency ω_p is well described by the power law ω_b～η _p ^4/3 ω _p ^23/9 .