Accurate Evaluation of the Cubic Lattice Green Functions Using Binomial Expansion Theorems

A new, simple, and efficient technique for the accurate evaluation of the lattice Green functions is presented. Using binomial expansion theorems, these functions are expressed through the binomial coefficients and basic integrals. The extensive test calculations show that the proposed algorithm in this work is the most efficient method in practical computations. Finally, in order to show the practical use of analytical expressions found some computation examples and comparisons with literature are made.     

Unified treatment for accurate and fast evaluation of the Fermi-Dirac functions

A new analytical approach to the computation of the Fermi-Dirac(FD) functions is presented,which was suggested by previous experience with various algorithms.Using the binomial expansion theorem,these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions.This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation,should such limits be required in practice.Some numerical results are presented for significant mapping examples and they are briefly discussed.     

Calculation of the Debye–Waller factor of crystals using the n-dimensional Debye function involving binomial coefficients and incomplete gamma functions

The objective of this work was to obtain a simpler and more accurate analytical expression to determine the Debye–Waller factor of crystals using an n-dimensional Debye approximation involving binomial coefficients and incomplete gamma functions. The results obtained were compared with the corresponding experimental and theoretical results and, the calculated values were shown to be in excellent agreement with those obtained in the experimental and other previous studies.     

Critical Comment on “Numerical solution of Bloch–Gruneisen function to determine the contribution of electron–phonon interaction in polycrystalline MgB2 superconductor” by Intikhab A. Ansari [Physica C: Superconductors, 470 (2010) 508–510]

We present critical comments on the recent paper [Intikhab A. Ansari, Physica C: Superconductors, 470 (2010) 508] concerning numerical methods for solving Bloch–Gruneisen function and its applications to MgB₂ superconductor. It is demonstrated that the presented in this work the formulas and examples are not original and they are quite identical the formulas already established in our article [B.A. Mamedov, I.M. Askerov, Physics Letters A, 362 (2007) 324].     

Evaluation of the generalized Goodwin-Staton integral using binomial expansion theorem

A new analytical technique for evaluating the generalized Goodwin-Staton integral (GGS) is described. A closed-form evaluation is presented. The GGS integral are expressed in terms of linear combinations of binomial coefficients and incomplete gamma function. A further comparison of analytical results with numerical models demonstrates a high accuracy of the developed analytical solution. The convergence of the results is shown.     

Excited Binomial States and Excited Negative Binomial States of the Radiation Field and Some of Their Statistical Properties

We introduce excited binomial states and excited negative binomial states of theradiation field by repeated application of the photon creation operator on binomialstates and negative binomial states. They reduce to Fock states and excitedcoherent states in certain limits and can be viewed as intermediate states betweenFock states and coherent states. We find that both the excited binomial statesand excited negative binomial states can be exactly normalized in terms ofhypergeometric functions. Base on this interesting characteristic, some of thestatistical properties are discussed.     

High-frequency conductivity of films with different surfaces

The high-frequency conductivity of films with different surfaces and spherically symmetric energy band is calculated. General expressions are obtained for the conductivity for arbitrary values of the following quantities: the film thickness, the frequencies of the incident wave, and the specularity parameters with allowance for the bulk scattering mechanisms. A detailed analysis is made of the influence of the boundedness of the sample and the different surfaces on the conductivity in limiting cases with respect to the film thickness and the frequency of the incident wave. In particular, it is shown that in the case of thin films and low frequencies the conductivity decreases with decreasing thickness. The influence of different surfaces on the conductivity is also considered. The dependence of the coefficient of absorption of the wave on the film thickness and the carrier density is analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 88–92, July, 1980.We are sincerely grateful to Professor B. M. Askerov for his interest in the work and a helpful discussion of the obtained results.     

Embedding sharp interfaces within the lattice Boltzmann method for fluids with arbitrary density ratios

Current lattice Boltzmann methods for simulating two fluids create a diffuse interface between the fluids. In this work, we develop a novel technique for embedding sharp interfaces between fluids with unbounded density ratios for the LB method. Distribution functions streamed across an interface are transformed so that the receiving node is passed information corresponding to its fluid phase. Two different methods are employed to determine the transformation. The first uses analytical distribution functions from steady Poiseuille flow to determine the jump in moments of the distribution functions across the interface. The second uses approximate expansions of distribution functions to determine jumps in distribution functions. The accuracy and stability of the methods are examined in simulations of Poiseuille-Couette flows with an interface parallel to the walls. Both methods show linear convergence to the analytical solution.     

Comparing energy difference and fidelity of quantum states

We look for upper bounds of the relative energy difference of two pure quantum states with a fixed fidelity between them or upper bounds of the fidelity for a fixed relative energy difference. The results depend on the concrete families of states chosen for the comparison. Exact analytical expressions are found for several popular sets of states: coherent, squeezed vacuum, binomial, negative binomial, and coherent phase states. Their consequence is that to guarantee, for example, a relative energy difference less than 10% for quite arbitrary (unknown) coherent states, the fidelity must exceed the level 0.995. For other kinds of states, the restrictions can be much stronger.     

Wigner functions and tomograms of the even and odd binomial states

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner functions of the even and odd binomial states (EOBSs) are obtained. The physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions. Moreover, the tomograms of the EOBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.     

Analytical evaluation of cylindrical exponential integrals arising in radiative transfer

New analytical results are presented performing to cylindrical exponential integral (CEI) functions for integer and noninteger values of parameter n. These integrals are often employed of two-dimensional radiative transfer in an absorbing-emitting medium and determination of the radiative flux in cylindrical media. The simple and efficient algorithm for the calculation of these functions is developed. The series expansion relations established in this work are accurate enough in the whole range of parameters.     

Inverse solutions to radiative-transfer problems based on the binomial or the Henyey-Greenstein scattering law

Analytical techniques are used to solve two inverse radiative-transfer problems, for a finite plane-parallel medium, that are (i) based on the binomial scattering law and (ii) based on the Henyey-Greenstein scattering law. In addition, previously reported analytical results (valid for isotropic scattering) that yield an analytical inverse solution for the unknown optical thickness of the medium are extended to the case of anisotropic scattering. The algorithms for the inversions are verified numerically, and some effects of noise on the simulated experimental data are observed.     

Mathematical Models for the Propagation of Stress Waves in Elastic Rods: Exact Solutions and Numerical Simulation

In this work, the Bishop and Love models for longitudinal vibrations are adopted to study the dynamics of isotropic rods with conical and exponential cross-sections. Exact solutions of both models are derived, using appropriate transformations. The analytical solutions of these two models are obtained in terms of generalised hypergeometric functions and Legendre spherical functions respectively. The exact solution of Love model for a rod with exponential cross-section is expressed as a sum of Gauss hypergeometric functions. The models are solved numerically by using the method of lines to reduce the original PDE to a system of ODEs. The accuracy of the numerical approximations is studied in the case of special solutions.     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.     

The radiation impedance of a rectangular piston

The radiation impedance of a rectangular piston is expressed as the Fourier transform of its impulse response, which is obtained from the recent work of Lindermann [1]. The analytical evaluation of the transform is performed and new integral expressions are presented for both the radiation resistance and reactance. The integrals are readily evaluated in terms of elementary functions at both the low and high frequency limits. The integrals are also expressed as series of Bessel functions which are valid for all frequencies and aspect ratios. Numerical results are presented to illustrate the behavior of the radiation resistance and reactance as a function of the aspect ratio of the piston and a normalized frequency parameter. Additional numerical results are then presented to illustrate the accuracy of the analytical expressions for the radiation resistance and reactance at low and high frequencies. Finally, numerical results are presented to illustrate the application and accuracy of using standard FFT algorithms to evaluate the radiation resistance and reactance directly from the impulse responses.     

Kinetics of the excited states of aromatic molecules in the presence of heavy atoms in rigid solutions

The response functions of the decay of the singlet and triplet states of aromatic molecules, in the presence of the heavy-atom perturbers in rigid solutions, are derived using a binomial distribution for averaging and assumption of additivity of the contributions from different perturber molecules. All processes involving the change of multiplicity are taken into account. Direct and indirect excitation modes and different monitoring modes are considered. The response functions and the relations between different luminescence characteristics considered here are valid for all concentrations of the perturber.     

Multiple-Photon-Added and -Subtracted Two-Mode Binomial States:Nonclassicality and Entanglement *

We theoretically analyze the nonclassicality and entanglement of two new non-Gaussian entangled states generated by applying multiple-photon addition and subtraction to a two-mode binomial state. The nonclassical properties are investigated in terms of the partial negativity of the Wigner functions, whose results show that their nonclassicality can be enhanced via one-mode even-number photon operations and two-mode symmetrical operations for the initial two-mode binomial state. We also find that there exists some enhancement in the entanglement properties in certain parameter ranges via one-mode photon-addition and two-mode symmetrical operations.     

Emission and absorption spectra of a Λ type three-level atom driven by a two-mode cavity field with nonlinearities

An analytical expression of the emission and absorption spectra for a Λ type three-level cavity-bound atom interacting with a two-mode cavity field is given using the dressed states of the system. We take into account explicitly the nonlinearities of both the field and the intensity-dependent atom-field coupling. The characteristics of the emission and absorption spectra when one of the two-mode cavity fields is in a binomial state and the other is in a squeezed coherent state are exhibited. The effects of the mean number of photons, detuning, and the kinds of nonlinearities on the spectra are analyzed.     

Quantum and classical binomial distributions for the charge transmitted through coherent conductor

We discuss controversial results for the statistics of charge transport through coherent conductors. Two distribution functions for the charge transmitted was obtained previously, one actually coincides with classical binomial distribution, the other is different, and we call it here quantum binomial distribution. We show that high-order charge correlators, determined by the either distribution functions, all can be measured in different setups. The high-order current correlators, starting with the third order, reveal (missed in previous studies) special oscillating frequency dependence on the scale of the inverted time flight from the obstacle to the measuring point. Depending on setup, the oscillating terms give substantially different contributions.     

Nonclassical properties and algebraic characteristics of negative binomial states in quantized radiation fields

We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Perelomov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they are excited geometric states. As intermediate states, they interpolate between the number states and geometric states. We also point out that they can be recognized as the nonlinear coherent states. Their nonclassical properties, such as sub-Poissonian distribution and squeezing effect are discussed. The quasiprobability distributions in phase space, namely the Q and Wigner functions, are studied in detail. We also propose two methods of generation of the negative binomial states. d 32.80.Pj Optical cooling of atoms; trapping Received 8 May 1999 and Received in final form 8 November 1999