On the static permittivity of the Coulomb system in the long-wavelength limit

The general expression for the static permittivity ε(q, 0) of the Coulomb system in the region of small wave vectors was derived based on exact limit relations. The relation obtained describes the function ε(q, 0) in both “metal” and “dielectric” states of the Coulomb system. On this basis, the concept of the “true” dielectric is introduced and the definition of the “true” screening length was discussed. Exact relations were derived for the function ε(q, 0) in the region of small wave vectors q within the random phase approximation at an arbitrary degeneracy.     

Decays of the mesons and the singlet photon

In an attempt to explain the recent measurements on the radiative decays of the vector-mesons (V→Pγ), we study the consequences of introducing a small admixture of SU (3) singlet piece in the electromagnetic current. We find that this leads to an excellent fit of the theory with the new measurements on theV→Pγ decays. However, this addition adversely affects the fit of the leptonic decays of the vector mesons (V→e ⁺ e ⁻) and of the radiative decay of the pion (π→2γ). We conclude that the overall fit to the available data does not favour a large (>10%) admixture of the SU(3) singlet. The decay rates have been calculated in the vectormeson dominance model. At the hadronic vertex (VVP), we assume asymptotic nonet symmetry. The electromagnetic couplings (V−γ) are the ones appropriate to vector-mixing.     

On the Residual Entropy of the Blume-Emery-Griffiths Model

By means of a transfer matrix method, we show that the residual entropy S of the two dimensional square lattice Blume-Emery-Griffiths model on the antiquadrupolar-disordered and ferromagnetic-antiquadrupolar-disordered phase boundaries satisfies the inequalities (ln λ _1,n )/(n+1)≤S≤(ln λ _1,n )/n, where λ _1,n is the largest eigenvalue of a transfer matrix F _n on a strip of width n. These bounds imply the existence of a O(1/n) correction in the approximation of S by (ln λ _1,n )/n. Using these bounds, we calculate numerically the value of S, with precise estimates on the errors.     

Radiative decays,photoproduction and total cross section of theψ particles

It is pointed out that the coupling characterizing theψ-γ vertex must change substantially between the limits,ψ on mass-shell which occurs inψ→e ⁺ e ⁻ and photon on mass-shell which is relevant in radiative decays likeψ→ππγ, ψ→ηγ and photoproduction ofψ. This has the consequence that the value ofψN total cross section must be larger than what is inferred from the use of naive vector dominance in photoproduction.     

Semiclassical asymptotics of the spectrum of a nonselfadjoint operator on the sphere

The asymptotics as ɛ → 0 of the spectrum of the shifted Laplace operator H = ɛΔ + ∂ _υ on the standard two-dimensional sphere is described, where υ is a vector field. Dedicated to the memory of Vladimir Borovikov     

Direct calculation of the probability of pionium ionization in the target

The goal of the DIRAC experiment at CERN is the lifetime measurement of pionium (π ⁺ π ⁻ atom). Its lifetime is mainly defined by the charge-exchange process π ⁺ π ⁻ → π ⁰ π ⁰. The value of the lifetime in the ground state is predicted in the framework of chiral perturbation theory with high precision: τ _1S = (2.9 ± 0.1) × 10⁻¹⁵ s. The method used by DIRAC is based on analysis of π ⁺ π ⁻-pair spectra with small relative momenta in their center-of-mass system in order to find out the signal from pionium ionization (breakup) in the target. Pioniums are produced in proton-nucleus collisions and have relativistic velocities (γ > 10). For fixed values of the pionium momentum and the target thickness, the probability of pionium ionization in the target depends on its lifetime in a unique way; thus, the pionium lifetime can be deduced from the experimentally defined probability of pionium ionization. On the basis of ionization cross sections of pionium with target atoms, we perform the first direct calculation of the pionium ionization probability in the target. The text was submitted by the author in English     

Influence of γ irradiation on the electrical conductivity and dielectric properties of β TlInS2 in the temperature range of the incommensurate phase

The influence of γ irradiation on the electrical conductivity σ, the dielectric permittivity ɛ, and the dielectric loss tangent tanδ of β-TlInS₂ crystals is investigated in the temperature range of the incommensurate phase. It is established that γ irradiation lowers the values of ɛ and tanδ over the entire investigated temperature range and decreases the maxima of the σ(T) and tanδ(T) curves in the vicinity of the transition temperature T _c, but does not alter the transition temperature. Fiz. Tverd. Tela (St. Petersburg) 39, 1088–1090 (May 1997)     

A global version of the quantum duality principle

The “quantum duality principle” states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal Poisson group and, conversely, a quantisation of a formal Poisson group yields a quantisation of the dual Lie bialgebra as well. We extend this to a much more general result: namely, for any principal ideal domainR and for each primepεR we establish an “inner” Galois’ correspondence on the categoryHA of torsionless Hopf algebras overR, using two functors (fromHA to itself) such that the image of the first and the second is the full subcategory of those Hopf algebras which are commutative and cocommutative, modulop, respectively (i.e., they are“quantum function algebras” (=QFA) and“quantum universal enveloping algebras” (=QUEA), atp, respectively). In particular we provide a machine to get two quantum groups — a QFA and a QUEA — out of any Hopf algebraH over a fieldk: apply the functors tok[ν] ⊗k H forp=ν. A relevant example occurring in quantum electro-dynamics is studied in some detail. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001     

Effect of plasmon-phonon excitations on the coefficient of reflection from the surface of hexagonal silicon carbide

The coefficient R(ν) of reflection from the surface of 6H-SiC single crystals is studied in the case in which the long-wavelength optical vibrations of the lattice are coupled with the electron plasma. It is shown for the first time that the anisotropy of the properties of electrons and phonons in 6H-SiC gives rise to special features in the spectrum of the coupled vibrations and the transparency regions. It is found, in particular, that if the axis of the crystal lies in the polarization plane of the incident radiation (0<θ<90°), for 30 cm⁻¹⩽ν _p⊥<320 cm⁻¹ the spectrum of R(ν) acquires three regions of transparency and opacity, and for ν _p⊥⩾320 cm⁻¹ four such regions, which are absent in an isotropic medium. The width of these regions is found to depend on the electron concentration in the conduction band and on the angle θ. Zh. éksp. Teor. Fiz. 116, 646–654 (August 1999)     

Testing the nature of the Λ(1520)-resonance in proton-induced production

The Λ(1520)-resonance has been recently studied in a unitarized coupled-channel formalism with πΣ(1385), KΞ(1530), ˉN and πΣ as constituents blocks. We provide a theoretical study of the predictions of this model in physical observables of the pp → pK⁺K^-p and pp → pK⁺π⁰π⁰Λ reactions. In particular, we show that the ratio between the π⁰π⁰Λ and K^-p mass distributions can provide valuable information on the ratio of the couplings of the Λ(1520)-resonance to πΣ(1385) and ˉN than the theory predicts. Calculations are done for energies which are accessible in an experimental facility like COSY at Jülich or the developing CSR facility at Lanzhou.     

Influence of the Epithermal Effects on the MCF Steady State

This work is devoted to the correct interpretation of the steady state parameters of the muon catalyzed fusion (MCF) process in a D/T mixture. Previously the influence of the epithermal effects dtμ-molecule formation by ‘hot,’ non-thermalyzed tμ-atoms) on the steady state parameters was studied only for measurements with a low-density target (density φ = 0.01 relative to the liquid hydrogen density). We suggest a new method allowing direct determination of the necessary corrections to the MCF cycling rate for high-density data (φ ≥ 0.4).     

A Dynamical Classification of the Range of Pair Interactions

We formalize a classification of pair interactions based on the convergence properties of the forces acting on particles as a function of system size. We do so by considering the behavior of the probability distribution function (PDF) P(F) of the force field F in a particle distribution in the limit that the size of the system is taken to infinity at constant particle density, i.e., in the “usual” thermodynamic limit. For a pair interaction potential V(r) with V(r→∞)∼1/r ^γ defining a bounded pair force, we show that P(F) converges continuously to a well-defined and rapidly decreasing PDF if and only if the pair force is absolutely integrable, i.e., for γ>d−1, where d is the spatial dimension. We refer to this case as dynamically short-range, because the dominant contribution to the force on a typical particle in this limit arises from particles in a finite neighborhood around it. For the dynamically long-range case, i.e., γ≤d−1, on the other hand, the dominant contribution to the force comes from the mean field due to the bulk, which becomes undefined in this limit. We discuss also how, for γ≤d−1 (and notably, for the case of gravity, γ=d−2) P(F) may, in some cases, be defined in a weaker sense. This involves a regularization of the force summation which is generalization of the procedure employed to define gravitational forces in an infinite static homogeneous universe. We explain that the relevant classification in this context is, however, that which divides pair forces with γ>d−2 (or γ<d−2), for which the PDF of the difference in forces is defined (or not defined) in the infinite system limit, without any regularization. In the former case dynamics can, as for the (marginal) case of gravity, be defined consistently in an infinite uniform system.     

Calculation of the Kirchhoff coefficients for the Helmholtz resonator

A Helmholtz resonator is a shell Ω_shell separating a compact cavity Ω_int from a noncompact outer domain Ω_out. A small opening Ω ^δ in the shell connects the cavity with the outer domain, causing the transformation of real eigenfrequencies of the Neumann Laplacian in the cavity into the complex scattering frequencies of the full spectral problem for the Neumann Laplacian on Ω = ℝ³\Ω_shell. The Kirchhoff model of 1882, see [21], gives a convenient ansatz

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

The Effect of the Number of Simulations on the Exponents Obtained by Finite-Size Scaling Relations of the Order Parameter and the Magnetic Susceptibility for the Four-Dimensional Ising Model on the Creutz Cellular Automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton using finite-size lattices with linear dimension 4≤L≤8. The exponents in the finite-size scaling relations for the order parameter and the magnetic susceptibility at the finite-lattice critical temperature are computed to be β=0.49(7), β=0.49(5), β=0.50(1) and γ=1.04(4), γ=1.03(4), γ=1.02(4) for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are consistent with the renormalization group predictions of β=0.5 and γ=1. The values for the critical temperature of the infinite lattice T _c (∞)=6.6788(65), T _c (∞)=6.6798(69), T _c (∞)=6.6802(70) are obtained from the straight-line fit of the magnetic susceptibility maxima using 4≤L≤8 for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are in very good agreement with the series expansion results of T _c (∞)=6.6817(15), T _c (∞)=6.6802(2), the dynamic Monte Carlo result of T _c (∞)=6.6803(1), the cluster Monte Carlo result of T _c (∞)=6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm result of T _c (∞)=6.6802632±5×10⁻⁵.     

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ ₀, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ ₀ r ², we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ ₀, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.     

A-dependence of the γ- and p-induced production of the Λ(1520) from nuclei

Using results of a recent calculation of the Λ(1520) in the nuclear medium, which show that the medium width is about five times the free width, we study the A-dependence of the Λ(1520) production cross-section in the reactions γA → K⁺Λ(1520)A^′ and pA → pK⁺Λ(1520)A^′. We find a sizable A-dependence in the ratio of the nuclear cross-sections for heavy nuclei with respect to a light one due to the large value of the Λ(1520) width in the medium, showing that devoted experiments, easily within reach in present facilities, can provide good information on that magnitude by measuring the cross-sections studied here.     

Measurement of light mesons at RHIC by the PHENIX experiment

The PHENIX experiment at RHIC has measured a variety of light neutral mesons (π ⁰, K _S ⁰, η, ω, η ^′, φ) via multi-particle decay channels over a wide range of transverse momentum. A review of the recent results on the production rates of light mesons in p + p and their nuclear modification factors in d + Au, Cu + Cu and Au + Au collisions at different energies is presented.     

Structure of turbulent flows of incompressible fluids and the parametrization of turbulence

The structure of stationary isotropic, homogeneous turbulence in an incompressible fluid with Re ≫ 1 set into motion by a force with amplitude f ₀ and spatial and temporal time scales of r ₀ and τ ₀, respectively, is examined. It is found that, depending on the magnitude of the force that sets the fluid into motion, three fundamentally different turbulent stationary states of the fluid can develop and the dimensionless parameters responsible for transitions from one state to another, γ=f ₀ τ ₀ ² /r ₀ and Γ=γ ^4/3 Re, are determined. It is shown that for γ≪1 and Γ≪1 a Kolmogorov spectrum with E(k)∝1/k ^5/3 develops in the inertial range. During the transition to turbulent flows driven by large amplitude forces f ₀, i.e., during the transition to a regime with γ≪1 and Γ ≫ 1, a segment of the spectrum with E(k)∝1/k ² develops near the viscous range and “detaches” the Kolmogorov spectrum from the viscous range. Further increases in the amplitude f ₀ of the force, i.e., approaching the parameter range with γ≫1 and Γ≫1, causes the entire inertial range to be “occupied” by a spectrum E(k)∝1/k ², and outside the inertial range, large scale structures with a characteristic size extending to γ ^2/5 r ₀ begin to be generated. In the regime with Γ≪1, the power dissipated per unit mass of fluid is independent of the viscosity, but on going to turbulent regimes with Γ≫1, the viscous losses begin to depend on the viscosity of the fluid. The “turn-off” of viscous dissipation for Γ≫1 shows that a drag crisis can occur simply as the source power is increased, without any further conditions. With this method for the excitation of turbulence, the Loitsyanskii integral diverges for arbitrary values of γ and Γ. A physical mechanism is proposed to explain the readjustment of the spectrum of the turbulent fluctuations at different γ and Γ. These results have all been obtained neglecting intermittency. Zh. éksp. Teor. Fiz. 116, 1630–1647 (November 1999)     

Influences on the pseudospin symmetry from the different fields of mesons in deformed nuclei

Influences from different fields of mesons on the pseudospin symmetry are investigated for deformed nuclei. The energy splitting between pseudospin partners are extracted from the relativistic mean field calculations. The results show that the σ-field contribution to the pseudospin energy splitting has nearly the same magnitude as the one obtained by the ω-field, but with opposite signs. The pseudospin energy splittings either for neutron or for protons are almost the same if the σ-field (V _σ ) and the ω-field (V _ω ) change at the same scale. The pseudospin energy splitting depends in the same way as the nucleus binding energy of the cancellation of these two potentials, and is controlled by the same nuclear physics scale as the potential sum V _ω + V _σ In comparison with the σ- and ω-fields, it is seen that the ρ meson field produces a minor influence on the pseudospin symmetry.