The asymptotic iteration method applied to certain quasinormal modes and non Hermitian systems

We study the Schrödinger equation with potentials admitting quasinormal modes using the asymptotic iteration method (AIM). We also study non-Hermitian PT symmetric potentials using AIM. The spectra, in all cases, are found to be in excellent agreement with exact results.     

Nonrelativistic ℓ-State Solutions for Schiöberg Molecular Potential in Hyperspherical Coordinates

The approximate analytical solutions of the N-dimensional Schrödinger equation for hyperbolic-type molecular potential, V(r) = D[1 ? σ coth(αr)]² are obtained by using asymptotic iteration method (AIM). The bound state energy eigenvalues and corresponding radial eigenfunctions are derived for arbitrary ?-states.     

On the fragmentation functions of heavy quarks into hadrons

An explicit form for the charmed quark fragmentation function D^C_c(z) into hadrons has been obtained with the help of the “reciprocity relation” and the c-quark distribution function in charmed mesons (the function calculated in terms of the Kuti-Weisskopf model). D^C_c(z) turns out to peak mainly at z close to 1. The analysis of new data on muon pair production in neutrino reactions points to such a behaviour of the D^C_c(z) function. The obtained fragmentation function, contrary to those, used earlier, leads to a charmed particle (average) multiplicity in e⁺e^?-annihilation independent of energy.     

Longitudinal Structure Function F L of Proton from Regge Like Behaviour of Structure Function at Small-x

The evolutions of longitudinal structure function F _L from quantum chromodynamics (QCD) evolution equation in next-to-leading order at small-x is presented using the Regge like behaviour of the structure function. The proposed simple analytical expression for F _L structure function provides the t- and x-evolution equations to study the behaviour of F _L structure function at small-x. The calculated results are compared with the data of H1, ZEUS collaborations and results of Block model, Donnachie–Landshoff model. Our calculated results can be described within the framework of perturbative QCD.     

A New Entropy Function to Analyze Isentropic Processes of Ideal Gases with Variable Specific Heats

A new entropy function s⁺ is defined in terms of the existing entropy function s° and temperature as s⁺ = s° − R lnT to facilitate the analysis of isentropic processes of ideal gases with variable specific heats. The function s⁺ also makes it possible to calculate the entropy changes of ideal gases during processes when volume information is available instead of pressure information and the variation of specific heats with temperature is to be accounted for. The introduction of the function s⁺ eliminates the need to use the dimensionless isentropic functions relative pressure P_r and relative specific volume v_r of ideal gases and to tabulate their values. The P_r and v_r data are often confused with pressure and specific volume, with an adverse effect on the study of the second law of thermodynamics. The new s⁺ function nicely complements the existing s° function in entropy change calculations: the former is conveniently used when volume information is given while the latter is used when pressure information is available. Therefore, the introduction of the new entropy function s⁺ is expected to make a significant contribution to the thermodynamics education and research by streamlining entropy analysis of ideal gases.     

Solution of Evolution Equation for Longitudinal Structure Function F L upto Next-to-Next-to-Leading Order and Its t-Evolution at Small-x

The aim of the present paper is to calculate longitudinal structure function F _L from QCD (Quantum Chromodynamics) evolution equation in next-to-next-to-leading order (NNLO) at small-x. The calculation of F _L is important for the phenomenological study of gluon distribution function inside the nucleon. Here we use Taylor Series Expansion method to solve the evolution equation for small-x and thus obtain t-evolution of F _L structure function. The calculated results are compared with H1 and ZEUS data and results of Block and Donnachie-Landshoff (DL) models.     

Sums of products of Coulomb wave function over degenerate states

The sums of products of Coulomb wave function over degenerate states are expressed in terms of quadratic forms that depend on the wave function of only one state with zero orbital angular momentum l = m = 0. These sums are encountered in many fields in the physics of atoms and molecules, for example, in investigations of the perturbation of degenerate atomic energy levels of a small potential well, a delta-function potential. The sums were found in an investigation of the limit of the Coulomb Green’s function G(r, r′, E), where the energy parameter E approaches an atomic energy level: E → E _n , E _n = ?Z ²/2n ². The Green’s function found by L. Hostler and R. Pratt in 1963 was used. The result obtained is a consequence of the degeneracy of the Coulomb energy levels, which in turn is due to the four-dimensional symmetry of the Coulomb problem.     

Electronic structure of the F-center in CaO and MgO

The energy levels and wave functions of the F-center in CaO and MgO have been calculated as function of the A_1g and E_g displacements of the nearest neighbor ions of the oxygen vacancy. In CaO, the calculated level scheme partially supports the interpretation of published experimental data on the luminescence bands but there are significant discrepancies. The localization of the wave function of the ³T_1u state is rapidly varying function of the A_1g lattice distortion. The present calculations give a Jahn-Teller splitting of this state of between 0.15 and 0.2 eV.     

Potential application of Al-doped ZnO nanotube as an electronic sensor for β-keto-amphetamine drug

The β-keto-amphetamine (β-KA) drug abuse causes numerous deaths worldwide. Thus, finding a proper sensor for β-KA drug detection is of great importance. Here, potential application of pristine and Al-doped ZnO nanotubes (ZN) was investigated in detection of β-KA using density functional theory calculations. Based on our AIM analysis, the β-KA drug physically adsorbed on the pristine ZN with adsorption energy (E_ad) of −4.7 kcal/mol. The sensing response of ZN to the β-KA drug is very small about 3.9 at 298 K. By substituting a Zn atom of ZN by an Al atom, the E_ad of β-KA drug increased to −22.9 kcal/mol and the nature of interaction changes from the physisorption to a highly polar covalent chemisorption. Also, the sensing response increased to 315.9, indicating that the Al-doping makes the ZN a promising sensor for β-KA. A recovery time of 19.0 s was predicted for the Al-ZN.     

Electron-phonon interactions and temperature dependence of infrared absorption in the conducting organic salt trimethylbenzimidazol-tetracyanoquinodimethane (TMB-TCNQ)

Infrared spectra of the simple salt TCNQ with trimethylbenzimidazol were studied vs temperature. The analysis of the mechanisms causing the absorption coefficient of the salt TMB-TCNQ to be dependent on temperature shows that three elements should be taken into account. The changes in electronic interactions described by the function W(T), the reduction of occupation of the ground state described by the function n_g(T), and the changes in geometry of the dimer described by the function D(T) are the main mechanisms defining the thermal dependences of the absorption coefficients. The electron-phonon coupling constants for different temperatures were determined.     

Relaxation function of a Heisenberg paramagnet at large wavevectors

An approach based on the Mori's theory to calculate the Kubo relaxation function is presented in order to explain the structure of neutron scattering cross section at large wavevectors for Heisenberg paramagnets. The limits of validity of the previous approximate theories are discussed. A low-frequency expansion for the third order memory function is performed: this corresponds to considering a more consistent long-time approximation for the second order memory function. The relaxation function has been computed for RbMnF₃ at T?T_N and T = 1.125T_N.     

Structures, chemical bonding, magnetisms of small Al-doped zirconium clusters

The geometrical and electronic properties of small Al-doped Zrn−1 and host Zrn clusters (n=2-8) are investigated with hybrid HF/DFT functional: B3LYP. For the most favorable configurations of Zrn−1Al clusters, the Al atom prefers to be located on the surface of host zirconium clusters. The isomers that correspond to low coordination number of Zr-Al bonds are found to be more stable. The doping of Al atom in Zrn−1 clusters improves the chemical activities of host clusters. The Zr₅, Zr₇, Zr₄Al and Zr₆Al clusters behave the stronger stabilities relative to their respective neighbors. The strong s-d hybridizations are presented in all bonding Zr atoms. The values of WBI together with AIM analysis suggest that the Zr-Zr interactions are stronger than those between Zr and Al atoms. The doping of Al atom results into the decrease of spin magnetic moments for host zirconium clusters. The moments are mainly derived from the 4d electrons of bonding Zr atoms.     

Analysis of the electroproduction structure functions in the lowQ 2 region,combining the vector meson dominance and the parton model with possible scaling violation

The nucleon structure functionF ₂ is constructed and analysed for low values ofQ ² using the generalised vector meson dominance representation with the largeQ ² spectral function calculated from the analytic continuation of the parton model structure function. Various parametrisations of the parton distributions are considered. Possible effects of the largeQ ² scaling violation on the lowQ ² part of the structure function are investigated. The magnitude of the total contribution given by this asymptotic part can be as high as 50% of the vector meson contribution in the low-Q ², low-χ region. The contribution of the valence quarks alone to the structure function at lowQ ² turns out to be at least as important as the corresponding non-Pomeron Regge-pole-like terms coming from the vector meson part. Increase of the structure function with ν coming from the increase of the quark sea in the limit of small χ implied by QCD turns out to be relatively weak at lowQ ². Predictions of the model are compared with available experimental data. The photoproduction cross section and the nuclear effects in the structure function are also briefly discussed.     

Self-similarity degree of deformed statistical ensembles

We consider self-similar statistical ensembles with the phase space whose volume is invariant under the deformation that squeezes (expands) the coordinate and expands (squeezes) the momentum. The related probability distribution function is shown to possess a discrete symmetry with respect to manifold action of the Jackson derivative to be a homogeneous function with a self-similarity degree q fixed by the condition of invariance under (n+1)-fold action of the related dilatation operator. In slightly deformed phase space, we find the homogeneous function is defined with the linear dependence at n=0, whereas the self-similarity degree equals the gold mean at n=1, and q→n in the limit n→∞. Dilatation of the homogeneous function is shown to decrease the self-similarity degree q at n>0.     

An approximation for rotation-projected expectation values of the energy for deformed nuclei and a derivation of the cranking variational equation

An approximation is given for the expectation value of the Hamiltonian with functions: where ¦?〉 is a HFB wave function of a deformed nucleus. This is achieved by expanding the overlap function of the energy 〈?¦ HD(Ω)¦?〉 in derivatives of the overlap function of the norm 〈? D(Ω)¦?〉. The cranking equations for even nuclei are yielded by varying the approximate energy.     

Effects of time-delay in stationary properties of a logistic growth model with correlated noises

A time-delayed tumor cell growth model with correlated noises is investigated. In the condition of small delay time, the stationary probability distribution is derived and the stationary mean value (〈x〉_st) and normalized varianceλ₂ of the tumor cell population and state transition rate (κ) between two steady states are numerically calculated. The results indicate that: (i) The delay time (τ) enhances the coherence resonance in 〈x〉_st as a function of the multiplicative noise intensity (D) and increases 〈x〉_st as a function of the additive noise intensity (α), i.e., τ enhances fluctuation of the system, however, the strength (λ) of correlations between multiplicative and additive noise plays a contrary role to τ on these; (ii) τ enhances the coherence resonance in κ as a function of D and increases κ as a function of α, i.e., τ speeds up the rate of state transition, however, λ also plays a contrary role to τ on these.     

Scaling in quantum gravity

The 2-point function is the natural object in quantum gravity for extracting critical behavior: The exponential falloff of the 2-point function with geodesic distance determines the fractal dimension d_H of space-time. The integral of the 2-point function determines the entropy exponent γ, i.e. the fractal structure related to baby universes, while the short distance behavior of the 2-point function connects γ and d_H by a quantum gravity version of Fisher's scaling relation. We verify this behavior in the case of 2d gravity by explicit calculation.     

The self-consistent determination of HF electroconductivity of strongly coupled plasmas

Here is presented the calculation of the dynamic electrical conductivity of fully ionized, strongly coupled plasmas as a function of the external electric field frequency ω. The calculations are based on the formula for the energy-dependent collision frequency which is determined by means of the Green function theory methods, as a sum over the Matsubara frequencies. The domain of extremely high electron density: ¹⁰²¹?ne?¹⁰²⁴ cm−3, and for the temperature varying from 10 kK to 1000 kK was examined. The real and imaginary parts of the conductivity for every electron density are presented in the generalized Drude-like form as a two-parameter function of the frequency ω in the region 0<ω<0.5ωp, where ωp is the plasma frequency. A good agreement between the obtained results and the existing theoretical and computing simulation data is shown.     

Comparison of the texture functions describing the grain alignment in NdFeB magnets

Two types of Gaussian distribution function (`θ type’ and `tan θ type') describing the degree of grain alignment in sintered NdFeB magnets have been compared in the distribution coefficient σ (or σ_g), the distribution probability P(θ) and the grain alignment dependence of coercivity. The results show that when the grain alignment is good (the ratio of remanence-to-saturation polarization J_r/J_s⩾0.90), σ(σ_g) and P(θ) for the two types of Gaussian functions have similar variation tendencies, the calculated values of normalized coercivity based on the starting field theory are basically the same and are consistent with experiments. When the grain alignment is not good (J_r/J_s⩾0.80), the variation tendencies of σ and P(θ) are different. In addition, according to `tan θ type’ Gaussian function, the theoretical values of the normalized coercivity based on the starting field theory are still consistent with the experiments, but according to `θ type’ Gaussian function, the theoretical values seriously deviate from the experiments. This means that the `tan θ type’ Gaussian function is a better texture function for describing the grain alignment.     

Investigation of the pion condensation threshold in finite nuclei

The threshold condition for pionic instabilities in finite nuclei is investigated by evaluating the response function for pion-like nuclear excitations (i.e. isovectorJ ^π =0^?, 1⁺, 2^?, ... excitations). The onset of pion condensation is then defined as the point where the response function for givenJ ^π becomes infinite at frequencyω=0. Using a momentum space representation for the response function which allows to establish clear connections to the nuclear matter case, we find that for angular momentaJ smaller than a maximum value which depends on the size of the nucleus, the threshold condition is almost the same as for infinite matter. We also study the systematics of this phenomenon as a function of nuclear mass number.