New features of a smectic-A-crystal-B phase transition in a homologous series of liquid crystals

The components L _j of the Lorentz tensor and the polarizability density of molecules G in the smectic-A and crystalline-B phases have been determined for homologues of the series of alkyl-p-(4-alkoxybenzylideneamino-)cinnamates. The quantity L _j (G) in both phases is a linear (quadratic) function of the orientational order parameter of molecules S, which is invariant (noninvariant) with respect to the A-B transition, which is manifested in the form of jumps δL _j and δG and enhancement of the G(S) dependence. An increase in the length of terminal molecular chains and weakening of interlayer correlation of molecules are accompanied by strengthening of the A-B transition of the first order and G(S) dependences in both phases together with an increase in δL _j and δG. Change δG and dependence G(S) in the B phase are related to change in the conformation (flattening) of aromatic molecular cores.     

Obliquely propagating magnetosonic waves in multicomponent quantum magnetoplasma

Linear properties of obliquely propagating magnetosonic waves (both fast and slow) in multicomponent (electron-positron-ion (e-p-i) and dust-electron-ion (d-e-i)) quantum magnetoplasma are studied. It is found that the quantum Bohm potential term significantly changes the propagation of fast and slow magnetosonic waves in both e-p-i and d-e-i quantum plasmas. The variation of the dispersion characteristics with the increase/decrease of positron concentration in e-p-i and dust concentration in d-e-i quantum magnetoplasma is explored. Finally, the effect of angle θ (that the ambient magnetic field makes with the x-axis) on the dispersion properties of magnetosonic waves in multicomponent quantum magnetoplasma is investigated. The relevance of the present investigation to the dense astrophysical environments and microelectronic devices is also pointed out.     

On the scaling factors α(z) and δ(z)

We introduce a new method to determine the scaling factors α(z) and δ(z) for the period-doubling route to chaos in dissipative systems, exemplified by the one-dimensional mapping x_n+1=1−λ∣x_n∣^z. With the help of the Feigenbaum universal functions g(x) and h(x) we derive the inequality α^z−α<δ(z)<α^z, implying in particular that δ(z) remains finite (≲30) in the limit z → ∞.     

Irreducible kernels and nonperturbative expansions in a theory with purem →m interaction

Recent results on the structure of theS matrix at them-particle threshold (m≧2) in a simplifiedm→m scattering theory with no subchannel interaction are extended to the Green functionF on the basis of off-shell unitarity, through an adequate mathematical extension of some results of Fredholm theory: local two-sheeted or infinite-sheeted structure ofF arounds=(mμ)² depending on the parity of (m?1)(ν?1) (where μ>0 is the mass and ν is the dimension of space-time), off-shell definition of the irreducible kernelU which is the analogue of theK matrix in the two different parity cases (m?1)(ν?1) odd or even, and related local expansion ofF, for (m?1)(ν?1) even, in powers of σ_β ln σ(σ=(mμ)²?s). It is shown that each term in this expansion is the dominant contribution to a Feynman-type integral in which each vertex is a kernelU. The links between the kernelU and Bethe-Salpeter type kernelsG of the theory are exhibited in both parity cases, as also the links between the above expansion ofF and local expansions, in the Bethe-Salpeter type framework, ofF _λ in terms of Feynman-type integrals in which each vertex is a kernelG and which include both dominant and subdominant contributions.     

Functional properties of quantum logics

A quantum logic is defined as a setL of functions from the set of all statesS into [0, 1] satisfying the orthogonality postulate: for any sequencea ₁,a ₂, ... of members ofL satisfyinga _i+a _j≤1 fori≠j there isb∈L such thatb+a ₁+a ₂+...=1. Every logicL is in a natural way an orthomodular σ-orthocomplemented partially ordered set (L, ≤, ′) with members ofS inducing a full set of measures onL. It is shown that a logicL is quite full if and only if (L,≤,′) is isomorphic to an orthocomplemented set lattice of subsets ofS. Sufficient conditions are given in order that a quite full logic be representable in the set of projection quadratic formsf(u)=(Pu, u) on a complex Hilbert space, or in the set of trace functionsf(A)=Trace (AP) generated by projectionsP, where the domain off is the set of non-negative self-adjoint trace operators of trace 1 in a complex Hilbert space.     

Pseudoscalar quarkonium exclusive decays to vector meson pair

The pseudoscalar quarkonia exclusive decays to light mesons still poses a challenge to the theoretical understanding of quarkonium properties in decay. In this work, we evaluate the processes of pseudoscalar heavy quarkonium decays into vector meson pairs, especially the helicity suppressed processes of ηb→J/ψJ/ψ and ηc→VV. In the framework of NRQCD, the branching fraction of Br[ηb→J/ψJ/ψ] are evaluated at the next-to-leading order of perturbative QCD; and within the light-cone distribution formalism, we calculate also the higher twist effects in these processes. Numerical results show that the higher twist terms contribute more than what from the NLO QCD corrections in the process of ηb→J/ψJ/ψ. It is found that the experimental results on ηc→VV are hard to be understood by merely the quark model and perturbative QCD calculation.     

Analysis of the lattice,strong coupling series for g0φ4 field theory in d dimensions

We analyze the renormalized strong coupling series for lattice g₀φ⁴ field theory which is a double series in x = M⁴a⁴/g₀a_4?dandy = 1/M²a², where M is the renormalized mass, a the lattice spacing, g₀ the bare coupling constant and d the dimension of space-time. We extrapolate to large y for fixed x by using a Padé-like extrapolation technique. We study the dimensionless renormalized coupling constant G/M^4?d and find that as we approach the continuum(x → 0, y → ∞) the entire spectrum of g₀ from zero to infinity can be studied. Our results for d = 1,2,3,4 based on a series in y up to y⁵ and in x up to x³ show that for fixed lattice spacing a, G/M^4?d is a monotonic function of g₀ ranging from zero at g₀ = 0 to a maximum at g₀ = ∞. Using the high temperature expansion results, we have also derived 9 terms in y on 8 lattices of dimension 1,2,3 and 4 for the linear term in x, and studied this series to see if one can see a breakdown in this monotonic behavior of G for large y. The analysis of this latter series is inconclusive.     

Thermal relaxation of charm in hadronic matter

The thermal relaxation rate of open-charm (D) mesons in hot and dense hadronic matter is calculated using empirical elastic scattering amplitudes. D-meson interactions with thermal pions are approximated by D^? resonances, while scattering off other hadrons (K, η, ρ, ω, K^?, N, Δ) is evaluated using vacuum scattering amplitudes as available in the literature based on effective Lagrangians and constrained by realistic spectroscopy. The thermal relaxation time of D-mesons in a hot π gas is found to be around 25-50 fm/c for temperatures T=150-180 MeV, which reduces to 10-25 fm/c in a hadron-resonance gas. The latter values, argued to be conservative estimates, imply significant modifications of D-meson spectra in heavy-ion collisions. Close to the critical temperature (Tc), the spatial diffusion coefficient (Ds) is surprisingly similar to recent calculations for charm quarks in the Quark-Gluon Plasma using non-perturbative T-matrix interactions. This suggests a possibly continuous minimum structure of Ds around Tc.     

On stationary convection and oscillatory motions in ferromagnetic convection in a ferrofluid layer

It is shown analytically that the ‘principle of the exchange of stabilities’ (PES), in general, is not valid in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries and hence a sufficient condition is derived for the validity of the PES. Upper bounds for the complex growth rate are then obtained. It is proved that the complex growth rate σ=σ_r+iσ_i (where σ_r and σ_i are, respectively, the real and imaginary parts of σ) of an arbitrary oscillatory motion of growing amplitude, in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries lies inside a semicircle in the right half of the σ_rσ_i-plane whose center is at the origin and ²(radius)=RM₁/P_r, where R is the Rayleigh number,M₁ is the magnetic number and P_r is the Prandtl number. Further, bounds for the case of rigid ferromagnetic boundaries are also derived separately.     

Ab-initio interpretation of 〈r−3〉 electronic quantities in the hfs of Mg I 3s 3p 3 P and1 P

It has been known for a long time that, in a two-electron arc spectrum, the properties of the³ P and¹ P terms of the lowests p configuration cannot be interpreted correctly in a pure-configuration model. Following the experimental determination of the hyperfine constantA(3s 3p ¹ P ₁) in Mg I by Kluge and Otten, this paper presents the ab-initio interpretation of the 〈r ^?3〉_3p hyperfine electronic quantities in 3s 3p through the use of the multiconfigurational Hartree-Fock method. It appears that taking into account the effects of the monoelectronic excitations 3s→nd, 2p→np and 3p→np leads to ab-initio evaluations in very good agreement with experiment. The case of the 3p→np excitation, to which Brillouin's theorem should apply in principle, is discussed. Using the same method, a refined evaluation is proposed for the nuclear electric-quadrupole moment of Mg²⁵ (Q=0.200 ± 0.01 barn).     

Exact solutions for a diffusion equation with a nonlinear external force

This work is devoted to investigate the solutions of the one-dimensional diffusion equation by taking the nonlinear external force F(x,t;ρ)=−k(t)x+K/x+κx|x|^α−1η[ρ(x,t)] into account. Our investigation is first performed by considering the case α=0 and η=1, which results in a Burgers like equation with a spatial and time dependent external force. After, we consider the case α≠0 and η=α+1 and show that the solution found may be expressed in terms of the q-exponential functions present in the Tsallis formalism. In addition, we also discuss the stationary solution for α and η arbitraries.     

On the Deser,Gilbert, Sudarshan representation for functions Wi(ν, q2)(i = 1, 2) describing the electroproduction process

The Deser, Gilbert, Sudarshan representation (D.G.S.R.) for the functions W_i(ν, q²) (i = 1,2) is considered as equations determining spectral functions h_i(a, α) via the values W_i(ν, q²) in the physical region of the electroproduction channel. It is shown that if W_i(ν, q²) obey the microcausality and spectrality conditions, then the equations for h_i(a, α) have solutions in the class of Schwartz temperated distributions and thereby the D.G.S.R. is proved. Formulae are obtained expressing spectral functions in the D.G.S.R. through the values of functions W_i(ν, q²) in the physical region of the electroproduction channel.     

Duality Theorems in Ergodic Transport

We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose ?? is the shift acting on Bernoulli space X={1,2,??,d}^?, and, consider a fixed continuous cost function c:X×X???. Denote by ?? the set of all Borel probabilities ?? on X×X, such that, both its x and y marginals are ??-invariant probabilities. We are interested in the optimal plan ?? which minimizes ??c? d?? among the probabilities in ??. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on c. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs c the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan ?? by convex combinations of plans such that the support projects in periodic orbits.     

An approach to radially symmetrical solutions of the sine-Gordon equation

The solution φ(r, t) of the radially symmetric sine-Gordon equation is considered in three and two spatial dimensions for initial curves, analogous to a 2π-kink, in the expanding and in the shrinking phase, for R(t)j? R(0). It is shown that the parameterization φ(r, t) = 4 arcian exp[γ(r?R(0)] + x(r, t), where R(t) describes the exact propagation of the maximum of φ,(r, t), is suitable. Using an appoximate differential equation, recently given for the propagation of the solitary ring wave, a rough analytic approximation for the correction function x(r = R(t), t) is found and tested numerically. A relationship between the fluctuations in x(r = R(t), t) and those in $\text{R}\text{?}\text{(t), t)}\text{and}\text{R(t)}$ explains why the solitary wave is almost stable. From x(r = R(t), t) and the supposition x(1, t) ≈ x(∞, t) ≈ 0 an assymetry in φ_r(r, t) with respect to r = R(t) is predicted. It also exhibits fluctuations corresponding to those in x(r = R(t), t). The condition for validity of this approximation apparently is also a limit for the stability of the solitary ring wave.     

Monte Carlo study of the Ising antiferromagnetic with a longitudinal field on the anisotropic square lattice

The Ising antiferromagnetic in the presence of a magnetic field on an anisotropic square lattice is studied by Monte Carlo simulation. We obtained the phase diagram in the T-H plane investigating the reentrant behavior around of the critical field Hc=2Jy. Using the Binder cumulant we locate the critical temperature Tc as a function of H. In order to test our simulation, for null field we obtain the critical behavior of Tc as a function of r=Jy/Jx and is in excellent agreement with exact solution of Onsager. Our results indicate a second-order transition for all values of H and particular case r=1 (independent of the ratio r≠0), where not reentrant behavior was observed.     

Supermultiplet symmetry and near-threshold levels in systems featuring two or three extremely light clusters

On the basis of the supermultiplet potential model for the interaction of extremely light clusters (formalism of Young diagrams), it is explained why the d+t system does not feature a (1/2)⁺(L=0) level allied to (3/2)⁺(L=0) thermonuclear resonance. By using known data on the quasielastic knockout of nucleons from the inner1s shell of light nuclei, a systematics of near-threshold states in the t+d+d, t+t+d, and t+t+t systems is constructed in terms of excited Young diagrams like {f}={322}. The emergence of similar states in going over from the d+d and t+t systems (which feature no such states) to the α+d+d, α+t+d, and α+t+t systems (where they appear owing to the binding effect of the alpha particle) is discussed. The three-cluster states being considered may be important not only for nuclear physics proper but also for nuclear astrophysics.     

Spin freezing properties in LaNi5-xFex

We report magnetic and transport measurements in the metallic pseudobinary compound LaNi_5-xFe_x, which show a Fe spin freezing. The magnetic phase diagram in the x-T plane is derived in the range 0 ⩽ x 1.2, 20 K ⩽ T ⩽ 300 K. Above a critical Fe concentration x_c ≈ 0.3, the system undergoes a superparamagnetic to long range ferromagnetic ordering at a finite temperature T. At lower concentrations, no long range spin ordering is observed, which suggests that x is the percolation threshold. Instead, a transition to a phase characterized by strong irreversibilities is observed at temperature T_f(x). Very strong ferromagnetic coupling interactions between Fe atoms are observed at low concentrations (x < x_c), which contrast with small values of T observed for x ∼ x_c. The results, together with the nature of the spin freezing are discussed in relation to the 2d character of the magnetic lattice.     

Unitary quantum groups,quantum projective spaces andq-oscillators

We discuss the parametrization of quantum groups in terms of independent operators. We find that this consideration leads to the parametrization ofSU _q(2) in terms of aq-oscillator plus a commuting phase. The commuting phase is naturally identified with the subgroupU(1) and the remaining cosetSU _q(2)/U(1)=CP _q(1) consists of aq-oscillator. For unitary quantum groupsSU _q (n), the analogous construction results in the quantum projective spaceSU _q(n+1)/U _q (n)=CP _q (n) being identified with then-dimensionalq-oscillator. This yields a nonlinear action of the quantum groupSU _q(n+1) on then-dimensionalq-oscillator.     

Analysis of the φ → γπη and φ → γπ 0 π 0 decays

We study interference patterns in the φ → (γa ₀+π ⁰ ρ) → γπη and φ → (γf ₀+π ⁰ ρ) → γπ ⁰ π ⁰ reactions. Taking into account the interference, we fit the experimental data and show that the background reaction does not distort the π ⁰ η spectrum in the decay φ → γπη everywhere over the energy region and does not distort the π ⁰ π ⁰ spectrum in the decay φ → γπ ⁰ π ⁰ in the wide region of the π ⁰ π ⁰-system invariant mass, π ^ππ > 670 MeV, or when the photon energy is less than 300 MeV. We discuss the details of the scalar meson production in the radiative decays and note that there are reasonable arguments in favor of the one-loop mechanism φ → K ⁺ K ^? → γa ₀ and φ → K ⁺ K ^? → γf ₀. We also discuss distinctions between the four-quark, molecular, and two-quark models and argue that the Novosibirsk data give evidence in favor of the four-quark nature of the scalar a ₀(980) and f ₀(980) mesons.     

Self-similarity of low-p T cumulative pion production in proton-nucleus collisions at high energies

The experimental data on inclusive spectra of the π⁺ mesons produced in p + A collisions at the incident proton momentum of 400 GeV/c obtained by G. Leksin group at FNAL are analyzed in the framework of z-scaling. Self-similarity of the hadron production in the low-p _T cumulative region is verified. Scaling function ψ(z) for the Li, Be, C, Al, Cu, Ta nuclei is constructed. It is expressed via the invariant cross section and average multiplicity density of charged particles. Results of the analysis of the low-p _T data are compared with the high-p _T data sets obtained by J. Cronin, R. Sulyaev and D. Jaffe groups. A microscopic scenario of p + A interactions in terms of momentum fractions x ₁, x ₂ is discussed. Indication on self-similarity of the cumulative pion production in p + A collisions over a wide kinematical range has been found. Based on the universality of the shape of the scaling function the inclusive cross sections of the π⁺ mesons produced in p + A collisions on the Li, Be, C, Al, Cu, Ta targets in deep-cumulative region (x ₂ ? 1/A) are predicted.