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.     

Coevolutionary extremal dynamics on gasket fractal

We considered a Bak-Sneppen model on a Sierpinski gasket fractal. We calculated the avalanche size distribution and the distribution of distances between subsequent minimal sites. To observe the temporal correlations of the avalanche, we estimated the return time distribution, the first-return time, and the all-return time distribution. The avalanche size distribution follows the power law, P(s)∼s−τ, with the exponent τ=1.004(7). The distribution of jumping sites also follows the power law, P(r)∼r−π, with the critical exponent π=4.12(4). We observe the periodic oscillation of the distribution of the jumping distances which originated from the jumps of the level when the minimal site crosses the stage of the fractal. The first-return time distribution shows the power law, Pf(t)∼t−τf, with the critical exponent τf=1.418(7). The all-return time distribution is also characterized by the power law, Pa(t)∼t−τa, with the exponent τa=0.522(4). The exponents of the return time satisfy the scaling relation τf+τa=2 for τf?2.     

Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(S_α(t)), 0<α<1, here dX(τ)=μX(τ)(dτ)^2H+σX(τ)dB_H(τ), as a model of asset prices, which captures the subdiffusive characteristic of financial markets. We find the corresponding subdiffusive Black-Scholes equation and the Black-Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.     

The rate matching effect: A hidden property of aperiodic stochastic resonance

We study a system S generating Poisson events, and a corresponding dichotomous signal as well, perturbed by a system P, also generating Poisson events and a corresponding dichotomous signal. The rates of events productions for system and perturbation are gS and gP, respectively. We call S events the events produced by the system S and P events those produced by the perturbation P. We show that this simple model reproduces the essence of recent experimental and theoretical results on aperiodic stochastic resonance. More remarkably, this simplified version of aperiodic stochastic resonance allows us to discover a property that has been overlooked by the earlier research work. The rate matching condition gS=gP is the border between two distinctly different conditions: For gS<gP, the P events are attractors of the S events and for gS>gP they become repellers of the S events. The transition from the former to the latter condition is very marked and takes place in a short region of either gS or gP, depending on which is the parameter changed, thereby resulting in a discontinuous transition.     

Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. III. Localization Properties

In this paper, we study the asymptotic localization properties with high probability of the Kth eigenfunction (associated with the Kth largest eigenvalue, K?1 fixed) of the multidimensional Anderson Hamiltonian in torus V increasing to the whole of lattice. Denote by z _K,V ∈V the site at which the Kth largest value of potential is attained. It is well-known that if the tails of potential distribution are heavier than the double exponential function and satisfies additional regularity and continuity conditions at infinity, then the Kth eigenfunction is asymptotically delta-function at the site z _τ(K),V (localization centre) for some random τ(K)=τ _V (K)?1. We study the asymptotic behavior of the index τ _V (K) by distinguishing between three cases of the tails of potential distribution: (i) for the “heavy tails” (including Gaussian), τ _V (K) is asymptotically bounded; (ii) for the light tails, but heavier than the double exponential, the index τ _V (K) unboundedly increases like |V|^o(1); (iii) finally, for the double exponential tails with high disorder, the index τ _V (K) behaves like a power of |V|. For Weibull’s and fractional-double exponential types distributions associated with the case (ii), we obtain the first order expansion formulas for logτ _V (K).     

Anomaly in the lattice partition function

The lattice partition function Z(T)=σ_(Si) exp(−H/k_BT), where H, k_B and T are the Hamiltonian of the system, the Boltzmann constant and the absolute temperature, respectively, leads to a vanishing spontaneous magnetisation for all temperatures, independently of the lattice considered. This feature is related to the symmetry breaking in these systems. In comparing this relation to the well-known partition function Z(T)=σ_n exp(−E_n/k_BT) where E_n is energy, we observe an incompatibility which could be the reason that this partition function leads to a vanishing spontaneous magnetisation.     

Interferometry for ellipso-height-topometry: Part 2: Measurement of the ellipsometric data, material identification, and correction of the measured height

Ellipso-height-topometry, EHT, as introduced by Leonhardt, et al. [Interferometry for ellipso-height-topometry, part 1, Optik 113 (2003) 513-519; Topometry for locally changing materials, Opt. Lett. 23 (1998) 1772-1774]; [Ellipso-height topometry, Optik 112 (2001) 413-420] is an extended topometry where topographies of the surface height H(x,y), the ellipsometric parameters Ψ(x,y) and Δ(x,y) (and optionally the intensity distribution I(x,y)) of the surface are measured on the same pixel raster and with high resolution. Thus, we can dispose over a set of (mutually coherent) topographies, and further topographies of quantities of interest can be calculated from this set: the local change in the complex refractive index N(x,y)=n(x,y)−k(x,y)i of bulk surfaces, the thickness distribution t(x,y) of locally changing (discontinuous) films and overlayers, and a correction of the optically measured local height H(x,y). The height error ΔH(x,y) can be calculated from the ellipsometric data and the true height h(x,y)=H(x,y)−ΔH(x,y) is thus obtained. ΔH(x,y) can assume large values when overlayers of oxidations or residues from lubrication oil or from processing are present. Much more information about the surface is gained with this concept.In part 1 of this work a z-scanning interferometric scheme with oblique incidence over the entire object field has been introduced, with the advantages of white-light interferometry, but with the additional capability of measuring material information to supply a complete set of topographies for extended topometry. In addition, very useful coherence properties for interferometry with oblique incidence were presented and discussed which allow to shape the interferogram in a simple way without any additional devices. In this part we derive the theory of the ellipsometric measurement and present first results by complete sets of two different samples.     

First passage time of multiple Brownian particles on networks with applications

In this article, we study some theoretical and technological problems with relation to multiple Brownian particles on networks. We are especially interested in the behavior of the first arriving Brownian particle when all the Brownian particles start out from the source s simultaneously and head to the destination h randomly. We analyze the first passage time (FPT) Y_sh(z) and the mean first passage time (MFPT) 〈Y_sh(z)〉 of multiple Brownian particles on complex networks. Equations of Y_sh(z) and 〈Y_sh(z)〉 are obtained. On a variety of commonly encountered networks, we observe first passage properties of multiple Brownian particles from different aspects. We find that 〈Y_sh(z)〉 drops substantially when particle number z increases at the first stage, and converges to d_sh, the distance between the source and the destination when z→∞. The distribution of FPT Prob{Y_sh(z)=t},t=0,1,2,… is also analyzed in these networks. The distribution curve peaks up towards t=d_sh when z increases. Consequently, if particle number z is set appropriately large, the first arriving Brownian particle will go along the shortest or near shortest paths between the source and the destination with high probability. Simulations confirm our analysis. Based on theoretical studies, we also investigate some practical problems using multiple Brownian particles, such as communication on P2P networks, optimal routing in small world networks, phenomenon of asymmetry in scale-free networks, information spreading in social networks, pervasion of viruses on the Internet, and so on. Our analytic and experimental results on multiple Brownian particles provide useful evidence for further understanding and properly tackling these problems.     

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.     

Stability for the Korteweg-de Vries equation by inverse scattering theory

The stability problems for the Korteweg-de Vries equation, where linear stability fails, are investigated by the inverse scattering method. A rather general solution u(t, x) of the K-dV equation is shown to depend, for fixed time t, continuously on the initial condition u(0, x). For a continuum solution u_c(t, x), this continuity holds uniformly in t (stability), but for a soliton solution this is not true. A soliton solution can be uniquely decomposed into a continuum and discrete (soliton) part: u(t, x) = u_e(t, x) + u_d(t, x). Then the perturbed solution u is close to u after a suitable t-dependent “shift” of the soliton part (form stability).     

The derivative nonlinear Schrödinger equation on the half-line

We analyze the derivative nonlinear Schrödinger equation on the half-line using the Fokas method. Assuming that the solution q(x,t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter ζ. The jump matrix has explicit x,t dependence and is given in terms of the spectral functions a(ζ), b(ζ) (obtained from the initial data q₀(x)=q(x,0)) as well as A(ζ), B(ζ) (obtained from the boundary values g₀(t)=q(0,t) and g₁(t)=q_x(0,t)). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation. Given initial and boundary values {q₀(x),g₀(t),g₁(t)} such that there exist spectral functions satisfying the global relation, we show that the function q(x,t) defined by the above Riemann-Hilbert problem exists globally and solves the derivative nonlinear Schrödinger equation with the prescribed initial and boundary values.     

Ecological interaction and phylogeny, studying functionality on composed networks

We study a class of composed networks that are formed by two tree networks, T_P and T_A, whose end points touch each other through a bipartite network B_PA. We explore this network using a functional approach. We are interested in how much the topology, or the structure, of T_X (X=A or P) determines the links of B_PA. This composed structure is a useful model in evolutionary biology, where T_P and T_A are the phylogenetic trees of plants and animals that interact in an ecological community. We make use of ecological networks of dispersion of fruits, which are formed by frugivorous animals and plants with fruits; the animals, usually birds, eat fruits and disperse their seeds. We analyse how the phylogeny of T_X determines or is correlated with B_PA using a Monte Carlo approach. We use the phylogenetic distance among elements that interact with a given species to construct an index κ that quantifies the influence of T_X over B_PA. The algorithm is based on the assumption that interaction matrices that follows a phylogeny of T_X have a total phylogenetic distance smaller than the average distance of an ensemble of Monte Carlo realisations. We find that the effect of phylogeny of animal species is more pronounced in the ecological matrix than plant phylogeny.     

Magnetic properties of transition metal substituted MnP

The magnetic properties of polycrystalline samples of Mn_1?tT_tP (T = V, Cr, Fe and Co for 0.00 ≦ t ≦ 0.50) are studied by magnetic susceptibility, magnetization and neutron diffraction measurements. The magnetic phase diagrams of the Mn_1?tT_tP phases exhibit paramagnetic, ferromagnetic, helimagnetic and spin glass regions depending on temperature and substitution (T, t). The concentrated spin glass regions observed in Mn_1?tV_tP and Mn_1?tCo_tP (0.30 ≦ t ≦ 0.50) are believed to result from the disorder in the metal sublattice. The variation of the magnetic moment of the ordered Mn_1?tT_tP phases with the substitution (T, t) is discussed.     

Interaction effects on atomic laboratory trapped Bose-Einstein condensates

We discuss the effect of inter-atoms interactions on the condensation temperature T _c of an atomic laboratory trapped Bose-Einstein condensate. We show that, in the mean-field Hartree-Fock and semiclassical approximations, interactions produce a shift Δ T _c /T _c ⁰ ≈ b ₁(a/λ _{T c} ) + b ₂(a/λ _{T c} )² + ψ[a / λ _{T c} ] with a the s-wave scattering length, λ _T the thermal wavelength and ψ[a / λ _{T c} ] a non-analytic function such that ψ[0] = ψ′[0] = ψ′′[0] = 0 and |ψ′′′[0]| = ∞. Therefore, with no more assumptions than Hartree-Fock and semiclassical approximations, interaction effecs are perturbative to second order in a / λ _{T c} and the expected non-perturbativity of physical quantities at critical temperature appears only to third order. We compare this finding with different results by other authors, which are based on more than the Hartree-Fock and semiclassical approximations. Moreover, we obtain an analytical estimation for b ₂ ? 18.8 which improves a previous numerical result. We also discuss how the discrepancy between b ₂ and the empirical value of b ₂ = 46 ± 5 may be explained with no need to resort to beyond-mean field effects.     

Current-voltage dependencies of heterogeneous semiconductor systems

Computed current-voltage (J–V) dependencies of heterogeneous (powder) semiconductor systems reveal an anomalous dependence between the constant-voltage current J and the uncompensated donor (acceptor) concentration N. Over a range of N(N₁ < n < N₂) of approximately one decade, J decreases by as much as four decades with increasing N. For N > N₂, the grain Schottky barrier thickness d is less than the grain half-width l/2, the grain surface potential V_s is almost independent of N and the J–V dependence is superlinear. For N₁ < N < N₂, d > l/2, V_s decreases linearly with N, J increases strongly with decreasing N and the J–V dependence is superlinear. For N < N₁, d > l/2. V_s ? V_th ( = kT/q) and J ∝ NV. The phenomenon is used to account for some observed J–V dependencies with column II-chalcogenide and ZnO powder semiconductor systems (electro-optic displays, electrophotographic receptors and heterogeneous catalysts).     

Components of the low-temperature heat capacity of rare-earth hexaborides

The temperature dependence of heat capacity C _p(T) was studied for nine rare-earth hexaborides MB₆(M=La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, and Dy) at temperatures of 5–300 K. Using the correspondence principle for lattice heat capacities of isostructural compounds, the lattice contribution C ₁(T) and the excess contribution ΔC(T) to the heat capacity of the hexaborides were determined. The lattice heat capacity C ₁(T) is represented as the sum of the Debye contributions of the metal and boron sublattices: C ₁(T)=C _M (T)+6C _B(T). The Debye temperatures π_M and π_B of the metal and boron sublattices were determined. The anomalies in the excess heat capacity ΔC(T)=C _p (T)?C ₁(T) are related to the magnetic ordering effects, the Schottky contribution, and the Jahn-Teller effect.     

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.     

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.     

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.