Relativistic bilocal lattice meson fields,divergence-free Green's functions and parton confinement

A bilocal lattice meson field equation which is invariant underP ₄×SO ₂×SO ₂×SO ₂×SO ₂, is investigated. A class of general solutions in terms of the Laguerre polynomials (products of 2-dimensional hydrogen atom wave-functions) is presented. The “atomic” wave-functions in “momentum”-space indicate that two particles (patrons) are in bound orconfined state and moving along elliptical orbits in “momentum”-space. Four Green's functions for the (bilocal lattice scalar) partialdifference equation are obtained. Theconvergence of one Green's function is rigorously proved and the convergence of others are conjectured.     

A study of Fe-doped Bi-Sr-Ca-Cu superconductors

We have substituted 1.5% of Fe for Cu in several “2212” and “2223” Bi-Sr-Ca-Cu superconductors. All of the samples show a reduction ofT _c about 13 K due to the Fe impurities. Mössbauer measurements at room temperature reveal the structural characteristics such as stacking faults and intergrowth of different phases in these Bi-based compounds on the microscopic scale. The susceptibility ofT _c to Fe-doping in the Bi-“2212” or “2223” system is comparable to that of the “123” system but much smaller than that of the “214” system. The interplanar correlation existing in the “123” and the Bi-“2212” and “2223” systems seems to play an important role in sustaining the high temperature superconductivity and weakening the detrimental effect of impurity elements on superconductivity in these two systems.     

MHD effects on the channel flow of a fractional viscous fluid through a porous medium: An application of the Caputo-Fabrizio time-fractional derivative

This research article considers the exact solutions and theoretical aspects of the channel flow of a fractional viscous fluid which is electrically conducting and flowing through a porous medium. Joint Laplace and Fourier transform techniques are used to solve the momentum equation. The Caputo-Fabrizio time fractional derivative is used in the constitutive equations. Exact solutions for an arbitrary velocity are obtained, and then in the limiting cases over a bottom plate three types of flow are considered: that is, the impulsive, accelerating and oscillating motion of the fluid. The case where the flow of the fractional fluid is unaffected by the side walls, is correspondingly taken into account. For oscillating flow the solutions are separated into steady and transient parts for both sine and cosine oscillations. Moreover these solutions are captured graphically, and the effect of the Reynolds number “Re”, fractional parameter “α”, effective permeability “K_eff” and the time “t”, on the fluid's motion are observed.     

The mass of the muon

It is shown that a classical relativistic charged particle has an anomalous magnetic moment g=4α/3. If such a “dressed” particle with its mass m, charge e, and anomalous magnetic moment g is quantized by a generalized Dirac equation, then the wave equation predicts a second mass m_μ=m_e(3/2α+1). It is suggested that a magnetic portion of the self-energy is quantized.     

Spin forbidden transitions in the Ka = 0 subband of NO2 in the λ = 592.5 nm region

In a high resolution laser excitation spectrum of NO₂, lines were recorded which do not follow the selection rule ΔN = ΔJ = ΔF of “spin allowed” transitions. Line positions and intensities of these “spin forbidden” lines were investigated for all rotational lines up to N″ = 12 of the K_a = 0 subband around λ = 592.5 nm. While the observed line intensities of “spin allowed” transitions can be well described by the J-coupling scheme, neither the J- nor the G-coupling scheme sufficiently describes the “spin forbidden” transitions. The observations can be fitted satisfactorily by perturbation theory, in which the Fermi interaction in ²A₁ is treated as the perturber. This looks similar to a superposition of J and G scheme in the ²A₁ ground state.     

Polymorphic transitions in molecular crystals—III.: Transitions exhibiting unusual behavior

Some polymorphic transitions in molecular crystals, among the few classified earlier as displacive or martensitic on the basis of the existence of a definite orientation relationship between the lattices of the phases and the “instantaneous” transformation rate, have been experimentally investigated. The investigation showed no evidence of a high rate of transition. All occurred through nucleation at the lattice imperfections and continuous growth of the new phase at a rate depending on ΔT = T_tr ? T_a, where T_tr is the actual transition temperature and T_o is the temperature of the thermodynamic equilibrium of the phases. The interface can be observed; its motion can be controlled, be done so slow as it is desirable, or be stopped. The “instantaneous transformations” reported in the literature are caused by temperature delays of nucleation in the absence of appropriate lattice defects. In reality these are polymorphic transitions which appear to be instantaneous only when observed through an optical microscope; actually they occur at the rate corresponding to ordinary temperature dependence. It was established that lamination or cleavage of the crystals in a definite direction is a common feature of the substances exhibiting “atypical” behavior. (Typical behavior has been described in [1,2]). The observed characteristics of the polymorphic transitions (uniform direction of the interfaces, definite orientation relationship of the lattices, small temperature hysteresis of the transition, etc.) can be readily explained in terms of epitaxial growth of the new phase on the cleavage planes of the original phase. At the same time the role of the proximity of crystal structural parameters is elucidated. Simple model calculations showed that a coherent interface may occur when the structural differences in the junction plane of the two phases are small, while in the other cases the contact interface described in [2] is energetically advantageous. However, a cooperative rearrangement at the coherent interface is rejected. There is not any evidence that polymorphic transitions in molecular crystals may occur by means of a “shift”, a “displacement”, a “deformation”, an “overturn”, etc. It is concluded that they always occur as a result of growth. The molecular mechanism of the growth in solids has been described in [2].     

Effect of nuclear irradiation on the superconducting transition temperatures of A-15 materials

A mechanism for the degradation of superconducting transition temperatures T_c by high energy nuclear irradiation in A-15 materials is proposed. The radiation is supposed to produce small “disordered” regions having a very low T_c, in a matrix having the original T_c of the material. The composite system has a well defined but lower T_c due to the proximity effect of the “disordered” regions.     

Anomalous acid proton self-diffusion in N(CH3)4HSO4 — A candidate for proton superionic conductivity

The appearance of a “liquid-like” proton T₂ component above 100°C and the relatively high value of the proton self-diffusion coefficient D = (5–8) × 10^-7cm²sec^-1 between 175°C and 200°C demonstrate the onset of a super-ionic state in N(CH₃)₄HSO₄. The ratio between the “liquid” and “solid” like components shows that acid protons are responsible for the high ionic conductivity.     

On the neutron charge radius and the new experiments proposed for the precise (n,e)-scattering length measurement

Strict comprehensive treating the generalized Dirak equation for nucleon in external electro-magnetic field argues quite clear that there is no physical reason to bring into consideration so-called “Foldy-term” while obtaining the neutron mean square charge radius < r _n ² >, caused by an electric charge distribution inside a nucleon, from the experimental value of the (ne) — scattering length b _ne , that term being, as a matter of fact, fictitious one. Consequently, the representing of the experimental quantity b _ne as a sum of “Foldy length” b _F and “intrinsic” one b_I, even so splitting the total value of < r _n ² > in “Foldy” and “intrinsic” < r _in ² >, turn out of having no profound physical sense, being rather ambiguous in actual fact. The formal phenomenological relation, originated from the generalized Dirak equation for nucleon, of the quantities b _ne , < r _n ² >, and neutron anomalous magnetic moment μ is inquired. Concise treating < r _n ² > in the frame-work of up-to-date nucleon cloudy bag model (CBM) is presented, no “Foldy term” being emerged, and < r _n ² >, calculated according this approach, provides b _ne -value which is in agreement with experimental result within accuracy of about 10%. On the other hand, the experimental b _ne -value proves to be described phenomenologically through solely the neutron anomalous magnetic moment μ with the same accuracy ～ 10%. Then the necessity of obtaining b _ne -value with more reliable accuracy then in previous experiments becomes obvious, corrections have to be reduced to the level of the precise declared. For these aims, two new proposed experiments have been Monte-Carlo modelled. The first renders the measurement of the energy dependence of an elastic scattering cross-section on ⁸⁶ Kr, having the unique small capture cross-section. The second one is to measure the energy dependence of neutron scattering angle anisotropy for natural Xe.     

Overall railway noise impact in the U.K.

As part of a British Rail (BR) “Environmental and Social Impact” study in 1975, an attempt at assessing the relative noise impact of rail and road transport was made; 24 hour L_eq in dB(A) units was adopted for the noise measure, as this appeared to give good correlation with “dissatisfaction” and permitted simple estimation of levels from traffic and location data. Five train types were defined, two classes of line, three regions of population density and three standard topographies. The base L_eq value for each traffic mix, line and population region could be established from BR survey data, and the propagation from topography and population (house) densities, to give the population subjected to each L_eq. The percentage “dissatisfied” at each L_eq was then applied to arrive at the total population “dissatisfied”, which was found to be 106 000. A similar approach applied to motorways and principal “A” roads gave 4480 000 “dissatisfied”.     

Essential restriction on the symmetry of a unified theory for the case of massive gluons

In unified gauge theories with massive “color” gluons, the physical requirement of maintaining “color” SU(3) as a global classification symmetry is shown to lead to the following restrictions: (i) the local unifying symmetry group must be of the form G_flavor?G_color; (ii) quarks are to be integer charged; (iii) the number of flavors is an integral multiple of the number of “colors”.     

X-ray and UV photoelectron-spectroscopic studies of pyridine adsorbed on evaporated nickel and palladium in the temperature range 140–385 k

The states of pyridine adsorbed on evaporated nickel and palladium films have been investigated as a function of temperature in the range 140–385 K by means of X-ray and UV photoelectron spectroscopy. At ～ 140 K, pyridine “N-bonded” on the metal surfaces gives C 1s and N 1s peaks whose binding energies are very close to those for condensed pyridine and “N-bonded” pyridine on pre-oxidized nickel. The high-lying valence orbitals, 2b₁ (π) and 1a₂ (π) + 7a₁ (n), of pyridine show shifts similar to those for the “N-bonded” molecule on pre-oxidized nickel. At ～ 290 K, “π-bonded” pyridine shows large shifts in the C 1s and N 1s peaks and in the high-lying valence orbitals, as observed for “π-bonded” benzene on nickel. The assignments of the adsorbed states are supported by work-function change data. A large proportion of pyridine converts from the “N-bonded” to the “π-bonded” form between 220 and 290 K. Formation of “α-pyridyl” is suggested at ～ 375 K on nickel.     

Temperature dependence of the upper critical field of superconducting alloys

The upper critical field,H _c2, is calculated in the temperature range close toT _c for arbitrary values of the mean free path 1. The method is to treat the fourth-order term in the linearized differential equation for the gap parameter as a perturbation to the harmonic oscillator equation. The Nambu-Tuan term, which determines the structure of the “clean-limit” and “dirty-limit” parts of the fourth-order term, is calculated by means of the ladder diagram technique for impurity interaction lines. The result is that the magnitude of the slope of the curveH _c2/√2H _c κ versust=T/T _c att=1 decreases monotonically from the value 0.41 to 0.12 as the ratio of the BCS coherence lengthξ ₀ to the mean free path 1 increases from 0 to ∞. For 1?ξ ₀ this slope is about 0.26.     

The B=2 sector of the Skyrme model in S3(L)

We consider baryon-number-two solutions to the Skyrme effective lagrangian on the surface of a hypersphere, S₃(L). At high densities we find solutions with “radially” uniform energy and baryon densities analogous to solutions previously found for the baryon-number-one problem on S₃(L) and for the dense matter problem in R₃. The density for this phase transition is essentially the same in the three cases. An interpretation of this phase transition as a simulation of “deconfinement” is offered.     

Is the glass transition in some super-cooled polyphenyls preceded by molecular cluster formation?

A recently reported anomalous behaviour of the positronium annihilation rate with temperature in certain super-cooled organic liquids is explained in terms of a simple free-volume model modified in the presence of molecular cluster formation. This model apart from showing the entropic origin of the phenomenon accounts for the existence of the transition temperature “T_r” much above the glass-transition temperature T_g. It also predicts for the threshold temperature “T_r” fo clusters to commence formation a value of 310_-7.0^+8.0 K as against the experimental value of 304 K for ortho-terphenyl.     

Macroscopic cell representation of density matrix equation and optimal choice of projectors by variational principle

We introduce a complete set of projectors on Liouvillespace and a “cell representation” of the equation of motion of the density matrixρ adjusted to the macroscopic observables of the system. Using a variational principle, the projector on the relevant density matrixρ _rel is determined by the postulate that the subdynamics ofρ _rel should include an optimal part of the Liouvillean?. The relation of the reduced subdynamics equation to wellknown master equations is investigated.     

Strict parabolicity of the multifractal spectrum at the Anderson transition

Using the well-known “algebra of multifractality,” we derive the functional equation for anomalous dimensions Δ _q , whose solution Δ = χq(q–1) corresponds to strict parabolicity of the multifractal spectrum. This result demonstrates clearly that a correspondence of the nonlinear σ-models with the initial disordered systems is not exact.     

Effect of a temperature gradient on the polarization distribution in the surface layer of TGS crystals

Effect of variable temperature gradients on the polarization of the surface layers of triglycine-sulphate (TGS) crystals has been analyzed. A fundamental difference in the impact of these gradients on the sample sides corresponding to the positive (“+” P _s ) and negative (“?” P _s ) yield of the polarization vector has been discovered. In particular, it has been found that repolarization of the surface layer under the impact of thermal radiation occurs only on the “?” P _s side.     

Relaxation in a Duffing potential

The solution of the equation of motion for a particle in a Duffing potential, V(x) = α₁x²/2 + α₂x⁴/4 (α₁, α₂ > 0) for arbitrary anharmonicity strength is characterized by the presence of odd frequencies which implies that velocity and position autocorrelation functions of such an oscillator in a microcanonical ensemble are also characterized by odd frequencies. It is, however, non-trivial to determine whether such “discrete” frequencies also characterize the autocorrelation functions in a canonical ensemble as discussed recently by Fronzoni et al. (J. Stat. Phys. 41 (1985) 553). We recover and extend upon the results of Fronzoni et al. to show analytically, via Mori-Lee theory, that “essentially discrete” (i.e. well-defined peaks with finite but “small” width) temperature-dependent frequencies characterize the autocorrelation functions in a canonical ensemble.     

On the geometrical aspects of electromagnetism,I

The trajectory of a charged test particle under a Lorentz force is obtained as the geodesic of a riemannian four dimensional manifold. Originally, the geodesic equation is nonlinear in some vector field A′_μ. The nonlinearity is traded in for the correct characteristic $\text{e}\text{m}$ of the test particle through a gauge condition, imposed upon A′_μ, which turns the geodesic into the fully covariant linear and gauge invariant Lorentz equation. Fitting the $\text{e}\text{m}$ ratio inside the gauge leaves F′_μν independent of $\text{e}\text{m}$ and allows its identification with the E.-M. tensor F_μν. This four dimensional approach allows the identification of the fifth coordinate used in Kaluza's geometrization |1,2|. The gauge function appears as the sum of Hamilton-Jacobi function plus an additional term, related to the “length” of the trajectory. It is this latter term which guarantees the correct “normalisation” of the $\text{e}\text{m}$ ratio.