Solution of twist-3 evolution equation in double logarithmic approximation in QCD

The solution of the DGLAP evolution equation for the twist-3 gluon operators is obtained in the double logarithmic approximation of QCD perturbation theory. The method used for the solution is similar to the reggeon field theory. The asymptotics of the twist-3 parton correlation function for small Bjorken variables x_B is found.Received: 5 February 2004, Published online: 23 April 2004     

Equations for the description of wave scattering by multi-valued random surfaces

We consider a scattering theory for multi-valued rough surfaces which cannot be described by the conventional equation of the type z = ζ(x,y). Both Dirichlet and Neumann problems are analyzed. Starting with Green's theorem we obtain a representation of the scattered field, the surface integral equation, and the extinction theorem for such surfaces. In contrast to conventional theory, these equations contain three random functions x = x(u ₁,u ₂), y = y(u ₁,u ₂), and z = z(u ₁,u ₂), where u ₁ and u ₂ are the parameters describing the surface. We introduce two scattering amplitudes S _± for describing the scattered wave above and below the surface. The extinction theorem, if formulated in terms of S _?, allows us to determine S _? for an arbitrary multi-valued surface and after this it becomes possible to derive a simple integral equation for surface sources. Knowledge of the surface sources allows us to find S ₊ by integration.     

Classical Poisson Structure for a Hierarchy of One–Dimensional Particle Systems Separable in Parabolic Coordinates

Abstract

We consider a hierarchy of many-particle systems on the line with polynomial potentials separable in parabolic coordinates. The first non-trivial member of this hierarchy is a generalization of an integrable case of the Hénon-Heiles system. We give a Lax representation in terms of 2 × 2 matrices for the whole hierarchy and construct the associated linear r-matrix algebra with the r-matrix dependent on the dynamical variables. A Yang-Baxter equation of dynamical type is proposed. Classical integration in a particular case is carried out and quantization of the system is discussed with the help of separation variables.     

A Ground Miniband Width of a Superlattice with Rectangular Quantum Wells versus Constructive Parameters

A convenient formula for the ground miniband width as a function of constructive parameters of the superlattice is derived from the solution of the Kronig–Penney equation using the perturbation theory. The conditions of applicability of this formula are verified for the GaAs/Al_xGa_1–x As superlattices used as infrared photodetectors.     

Thermal diffusion of envelope solitons on anharmonic atomic chains

We study the motion of envelope solitons on anharmonic atomic chains in the presence of dissipation and thermal fluctuations. We consider the continuum limit of the discrete system and apply an adiabatic perturbation theory which yields a system of stochastic integro-differential equations for the collective variables of the ansatz for the perturbed envelope soliton. We derive the Fokker-Planck equation of this system and search for a statistically equivalent system of Langevin equations, which shares the same Fokker-Planck equation. We undertake an analytical analysis of the Langevin system and derive an expression for the variance of the soliton position Var[x _s ] which predicts a stronger than linear time dependence of Var[x _s ] (superdiffusion). We compare these results with simulations for the discrete system and find they agree well. We refer to recent studies where the diffusion of pulse solitons were found to exhibit a superdiffusive behaviour on longer time scales.Received: 28 June 2004, Published online: 26 November 2004PACS: 05.10.Gg Stochastic analysis methods - 05.45.Yv Solitons - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.50. + q Lattice theory and statistics     

Transport, optical and magnetotransport properties of hetero-epitaxial InAsxSb1−x/GaAs(x0.06) and bulk InAsxSb1−x (x0.05) crystals: experiment and theoretical analysis

We briefly review the growth and structural properties of InAs_xSb_1−x (x0.05) bulk single crystals and InAs_xSb_1−x (x0.06) epitaxial films grown on semi-insulating GaAs substrates. Temperature-dependent transport measurements on these samples are then correlated with the information obtained from structural (XRD, TEM, SEM) and optical (FTIR absorption) investigations. The temperature dependence of mobility and the Hall coefficient are theoretically modelled by exactly solving the linearized Boltzmann transport equation by inversion of the collision matrix and the relative role of various scattering mechanisms in limiting the low temperature and 300 K mobility is estimated. Finally, the first observation of Shubnikov oscillations in InAsSb is discussed.     

Convergence to SPDEs in Stratonovich Form

We consider the perturbation of parabolic operators of the form ∂ _t  + P(x, D) by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the solution to the random equation is affected by the randomness at the leading order. We show that, when the dimension is smaller than the order of the elliptic pseudo-differential operator P(x, D), the perturbed parabolic equation admits a solution given by a Duhamel expansion. Moreover, as the correlation length of the potential vanishes, we show that the latter solution converges in distribution to the solution of a stochastic parabolic equation with multiplicative noise that should be interpreted in the Stratonovich sense. The theory of mild solutions for such stochastic partial differential equations is developed. The behavior described above should be contrasted to the case of dimensions larger than or equal to the order of the elliptic pseudo-differential operator P(x, D). In the latter case, the solution to the random equation converges strongly to the solution of a homogenized (deterministic) parabolic equation as is shown in [2]. A stochastic limit is obtained only for sufficiently small space dimensions in this class of parabolic problems.     

A theoretical and numerical evaluation of the steady-state burning rate of vertically oriented PMMA slabs

The steady state burning rate of vertically oriented slabs of poly-methyl-methacrylate (PMMA) is numerically investigated. Model predictions are compared with measurements and results of the laminar boundary layer (LBL) theory. The numerical model provides a solution of the Favre-averaged Navier–Stokes equations coupled with sub-models for turbulence, combustion, soot production and radiation. The modelling of condensed phase processes is based on the one-dimensional heat transfer equation and pyrolysis is treated as a phase change using the latent heat approach. Results show that the pyrolysing region can be divided into three regions. In the laminar part of the flow (Gr _x < 4.3 × 10⁷), the predicted normalised burning rate, [mdot]″ _p x/μ_∞, is a power-law function of Gr _x with an exponent close to that of the LBL theory, surface re-radiation being the primary source of discrepancies. From the LBL theory for free flow, it is demonstrated that the local burning rate is inversely proportional to the shear velocity gradient. This is globally confirmed by numerical model results. At Gr _x = 4.3 × 10⁷ the change in slope of the burning rate observed experimentally, which indicates the end of the laminar flow region, is reproduced numerically. From Gr _x = 2.5 × 10⁹ model results show that the surface mass flux of pyrolyzate increases with x, in agreement with experimental data in literature.     

Solution of Ornstein-Zernike equation for wall-particle distribution function

The Ornstein-Zernike (OZ) equation is considered for the wall-particle distribution functiong ₀(x) in the case of a flat, impenetrable wall atx = 0 and a fluid of hard-core particles whose centers are constrained by the wall to occupy the semiinfinite spacex >/2, where is the particle diameter. A solution is given in terms of the wall-particle direct correlation function c₀(x) forx >/2, the bulk-fluid direct correlation function c_B (t), and p_B, the average bulk density. Explicit formulas for the contact surface density, total excess surface density, and the Laplace transform of the fluid density near the wall are given. For mean spherical type approximations, c₀ (x) forx >/2 and c_B (t) are both prescribed functions; for this case, a closed-form solution is obtained. An example is discussed and additional equations that enable one to go beyond the approximations considered above are introduced.Report #270, February 1976.The observation of this paper that the wall-particle problem can be treated using standard Wiener-Hopf techniques was independently made by Percus in his work, which came to our attention too late to be compared to, or incorporated into, our own results here.     

Drell–Yan production at small qT, transverse parton distributions and the collinear anomaly

Using methods from effective field theory, an exact all-order expression for the Drell–Yan cross section at small transverse momentum is derived directly in q _T space, in which all large logarithms are resummed. The anomalous dimensions and matching coefficients necessary for resummation at NNLL order are given explicitly. The precise relation between our result and the Collins–Soper–Sterman formula is discussed, and as a by-product the previously unknown three-loop coefficient A ⁽³⁾ is obtained. The naive factorization of the cross section at small transverse momentum is broken by a collinear anomaly, which prevents a process-independent definition of x _T -dependent parton distribution functions. A factorization theorem is derived for the product of two such functions, in which the dependence on the hard momentum transfer is separated out. The remainder factors into a product of two functions of longitudinal momentum variables and x_T²x_{T}^{2}, whose renormalization-group evolution is derived and solved in closed form. The matching of these functions at small x _T onto standard parton distributions is calculated at O(a_s)\mathcal{O}(\alpha_{s}), while their anomalous dimensions are known to three loops.     

Effective theory of NN interactions in a separable representation

We consider the effective field theory of the NN system in a separable representation. The pionic part of the effective potential is included nonperturbatively and approximated by a separable potential. The use of a separable representation allows for the explicit solution of the Lippmann-Schwinger equation and a consistent renormalization procedure. The phase shifts in the ¹ S ₀ channel are calculated to subleading order.     

Fermionization,Convergent Perturbation Theory,and Correlations in the Yang–Mills Quantum Field Theory in Four Dimensions

We show that the Yang–Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When a further momentum cutoff is imposed, this Fermionic theory has a convergent perturbation expansion. To zeroth order in this perturbation expansion, the correlation function E(x,y) of generic components of pairs of connections is given by an explicit, finite-dimensional integral formula, which we conjecture will behave as

Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid

We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter 3.0 ⩽ x₀ ⩽ 4.0 in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of x₀ considered by us on increasing the density while the nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase x₀. The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement.     

Density-functional theory investigation of energy gaps and optical properties of Hg1-xCdxTe and In1-xGaxAs

We use a modified Becke-Johnson exchange plus a local density approximation correlation potential within the density functional theory to investigate the electronic structures of Hg_1-xCd_xTe and In_1-xGa_xAs with x being 0, 0.25, 0.5, 0.75, and 1. For both of the two series, our calculated energy gaps and dielectric functions (real part ε₁ and imaginary part ε₂) are in agreement with the corresponding experimental results with x being between 0 and 1. The calculated zero-frequency refractive index varies greatly with x for Hg_1-xCd_xTe, but changes little with x for In_1-xGa_xAs, which is consistent with the real parts of their dielectric functions. Therefore, this new approach is satisfactory to describe the electronic structures and the optical properties of the semiconductors.     

In-plane magnetic penetration depth in FeSe1-xSx (x = 0, 0.04, 0.09) and FeTe1-xSex (x = 0.40) single crystals

The magnetization anomaly of FeSe_1–xS_x(x?=?0, 0.04, 0.09) and FeTe_1–xSe_x(x?=?0.40) single crystals are examined through our Modified Phenomenological Ginzburg–Landau (MPGL) theory applicable to two-band superconducting systems. The theory in the London limit calculates the values of λ_ab(0) as 445.695, 372.058 and 432.957?nm of FeSe_1–xS_x for x?=?0, 0.04, 0.09 which are very close to the experimental values reported by Hafiez et al. [Superconducting properties of sulfur-doped iron selenide. Phys Rev B. 2015;91(16):165109–165120] and as 534?nm for FeTe_1–xSe_x(x?=?0.40) single crystal, which is close to the experimental value reported by Yadav and Paulose [Upper critical field, lower critical field and critical current density of FeTe_0.60Se_0.40 single crystals. New J Phys 2009;11:103046]. In addition, the variation of temperature-dependent in-plane magnetic penetration depth λ_ab(T) with the temperature (T) has been presented, which agrees well as reported by Hafiez et al. [Superconducting properties of sulfur-doped iron selenide. Phys Rev B. 2015;91(16):165109–165120] and Yadav and Paulose [Upper critical field, lower critical field and critical current density of FeTe_0.60Se_0.40 single crystals. New J Phys. 2009;11:103046].     

Properties of Perturbative Solutions of Unilateral Matrix Equations

A left-unilateral matrix equation is an algebraic equation of the form a ₀+a ₁ x+a ₂ x ²+·+a _n x ⁿ =0 where the coefficients a _r and the unknown x are square matrices of the same order and all coefficients are on the left (similarly for a right-unilateral equation). Recently certain perturbative solutions of unilateral equations and their properties have been discussed. We present a unified approach based on the generalized Bezout theorem for matrix polynomials. Two equations discussed in the literature, their perturbative solutions and the relation between them are described. More abstractly, the coefficients and the unknown can be taken as elements of an associative, but possibly noncommutative, algebra.     

Central Limit Theorems for Nonlinear Hierarchical Sequences of Random Variables

Let a random variable x ₀ and a function f:[a, b] ^k [a, b] be given. A hierarchical sequence {x _n :n=0, 1, 2,...} of random variables is defined inductively by the relation x _n =f(x _{n–1, 1}, x _{n–1, 2}..., x _{n–1, k} ), where {x _{n–1, i} :i=1, 2,..., k} is a family of independent random variables with the same distribution as x _n–1. We prove a central limit theorem for this hierarchical sequence of random variables when a function f satisfies a certain averaging condition. As a corollary under a natural assumption we prove a central limit theorem for a suitably normalized sequence of conductivities of a random resistor network on a hierarchical lattice.     

Analysis of the Al content in semiconductor materials by null ellipsometric spectrometry

In this paper, we demonstrate two methods by which the aluminum content in Al_xGa_0.51−xIn_0.49P and Si-doped Al_xGa_0.51−xIn_0.49P film deposited on GaAs substrates by MOVCD can be measured nondestructively. The first method is to calculate the Al content by means of effective medium approximation theory based on the optical parameters of the samples determined from ellipsometric spectrometry at room temperature for different wavelengths. The second method is to obtain the values of the energy gap E_g by analyzing the third derivatives of the imaginary part of the dielectric function. The aluminum content in the samples is then evaluated by substituting the value of E_g into the linear interpolation equation. The results of both methods agreed well with that obtained by the energy dispersive X-ray analysis method.     

A convenient band-gap interpolation technique and an improved band line-up model for InGaAlAs on InP

The band-gap energy and the band line-up of InGaAlAs quaternary compound material on InP are essential information for the theoretical study of physical properties and the design of optoelectronics devices operating in the long-wavelength communication window. The band-gap interpolation of In_1−x−y Ga _x Al _y As on InP is known to be a challenging task due to the observed discrepancy of experimental results arising from the bowing effect. Besides, the band line-up results of In_1−x−y Ga _x Al _y As on InP based on previously reported models have limited success by far. In this work, we propose an interpolation solution using the single-variable surface bowing estimation interpolation method for the fitting of experimentally measured In_1−x−y Ga _x Al _y As band-gap data with various degree of bowing using the same set of input parameters. The suggested solution provides an easier and more physically interpretable way to determine not only lattice matched, but also strained band-gap energy of In_1−x−y Ga _x Al _y As on InP based on the experimental results. Interpolated results from this convenient method show a more favourable match to multiple independent experiment data sets measured under different temperature conditions as compared to those obtained from the commonly used weighted-sum approach. On top of that, extended framework of the model-solid theory for the band line-up of In_1−x−y Ga _x Al _y As/InP heterostructure is proposed. Our model-solid theory band line-up result using the proposed extended framework has shown an improved accuracy over those without the extension. In contrast to some previously reported works, it is worth noting that the band line-up result based on our proposed extended model-solid theory has also shown to be more accurate than those given by Harrison’s model.     

Where do the H atoms reside in PdH x systems?

We present an ab initio density-functional theory study of PdH _x systems. We evaluated the total energy of PdH _x systems with the H atoms occupying interstitial (octahedral and tetrahedral) sites of a Pd supercell, allowing for the relaxation of the coordinates and supercell dimensions. The majority of our calculations were based on supercells consisting of four Pd atoms, and up to four H atoms, covering the range from x = 0.25 to x = 1. In addition some larger calculations are reported. In order to compare the relative stability of systems at different values of x (at fixed pressure and temperature T = P = 0), we computed the enthalpy of formation ΔH _f (x) of the (non)stoichiometric systems. In the regime x = 0 → 1, the ΔH _f (x) decrease in a manner indicative of the existence of attractive interactions between the dissolved H atoms. Ideal-solution theory cannot be applied to this system. Furthermore, we find that tetrahedral occupation is favoured over octahedral occupation at high x, leading to the formation of a zincblende structure at x = 1. A preliminary vibrational analysis of normal modes has been performed. Inclusion of vibrational zero-point energies in a harmonic approximation leads us to conclude, tentatively, that the observed stability of octahedral site occupation is due to more favourable zero-point energies of the H atoms in those sites. The results indicate that a proper understanding of this system must take into account the quantum nature of the dissolved hydrogen.