On the computation of molecular auxiliary functions A n and B n

Molecular auxiliary functions A _n (p) and B _n (pt), arising in the Hartree-Fock-Roothaan (HFR) approximation for molecules, Ewald’s crystal lattice theory, electromagnetic stopping theory, and other approximate methods, are evaluated and analysed in the range of 17≤n≤60 and 25≤pt≤60.     

A Remark on the Residual Entropy of the Antiferromagnetic Ising Model in the Maximal Critical Field

By means of a transfer matrix method, we show that the residual entropy S of the two-dimensional square lattice antiferromagnetic Ising model in the maximal critical field satisfies (ln λ _n )/(n+1)≤S≤(ln λ _n )/n, where λ _n is the largest eigenvalue of the transfer matrix F _n on a strip of width n. Using these bounds, we numerically calculate the value of S, with precise estimates on the errors, namely, S=0.394198±0.020747.     

Comment: “On the computation of molecular auxiliary functions<Emphasis Type="Italic">A</Emphasis><Subscript>n</Subscript>and<Emphasis Type="Italic">B</Emphasis><Subscript>n</Subscript>”

Guseinov, Mamedov, Kara and Orbay (Pramana - J. Phys. 56, 691 (2001)) propose methods for evaluating the molecular auxiliary functionsA _n(p) andB _n(pt) for the range 17 ≤n ≤ 60 and 25 ≤pt ≤ 60. However, their procedure forA _n(p) is not new, and that forB _n(pt) is less efficient for their target range than another well-known method. Their approach does have merit for smaller non-zero values ofpt. Two minor errors in table 1 of their paper are also identified.     

In-plane propagation of millimeter waves in periodic magnetoactive semiconductor structures

Non-transmission bands of electromagnetic waves propagating along the layers in periodic structures are studied in the steady magnetic field perpendicular both to the uniaxis and the direction of propagation. The band control range (36÷75 GHz) inn-InSb/Al₂O₃ structures with the carrier densities 4 10¹³ ≤n ≤ 8 10¹⁴ cm⁻³ in magnetic fieldsB _o ≤ 2 T at temperatures 77 ≤T ≤ 200 K is found to agree with the calculated in the effective medium approximation. Attenuation down to −50 dB within the band is observed. The band lineshape is found to indicate additional effects related to the finite layer thickness and periodicity termination predicted by a more rigorous theory of dispersion.     

Precise model approximation of JINR (Dubna) data on nuclear level densities in the region 40 ≤ <Emphasis Type="Italic">A</Emphasis> ≤ 200 below <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The experimental nuclear level density below the neutron binding energy B _n in the mass region 40 ≤ A ≤ 200 is approximated to a high precision on the basis of the Strutinsky model combined with the assumption that the coefficient of collective enhancement of the level density for a given number of excited quasiparticles decreases exponentially with increasing excitation energy. This combination of model concepts makes it possible to reproduce faithfully not only the general trend revealed by the method developed at the Joint Institute for Nuclear Research (JINR, Dubna) in the change in the level density with increasing excitation energy in any nuclei but also the fine structure of this level density. Realistic experimental information about the change in the relationship between the densities of quasiparticle- and vibrational-type states was obtained for the first time for any nuclei virtually up to the neutron binding energy B _n .     

On the Residual Entropy of the Blume-Emery-Griffiths Model

By means of a transfer matrix method, we show that the residual entropy S of the two dimensional square lattice Blume-Emery-Griffiths model on the antiquadrupolar-disordered and ferromagnetic-antiquadrupolar-disordered phase boundaries satisfies the inequalities (ln λ _1,n )/(n+1)≤S≤(ln λ _1,n )/n, where λ _1,n is the largest eigenvalue of a transfer matrix F _n on a strip of width n. These bounds imply the existence of a O(1/n) correction in the approximation of S by (ln λ _1,n )/n. Using these bounds, we calculate numerically the value of S, with precise estimates on the errors.     

Dynamic Critical Behavior of the Chayes–Machta Algorithm for the Random-Cluster Model,I. Two Dimensions

We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes–Machta dynamics for the Fortuin–Kasteleyn random-cluster model, which generalizes the Swendsen–Wang dynamics for the q-state Potts ferromagnet to non-integer q≥1. We consider spatial dimension d=2 and 1.25≤q≤4 in steps of 0.25, on lattices up to 1024², and obtain estimates for the dynamic critical exponent z _CM. We present evidence that when 1≤q≲1.95 the Ossola–Sokal conjecture z _CM≥β/ν is violated, though we also present plausible fits compatible with this conjecture. We show that the Li–Sokal bound z _CM≥α/ν is close to being sharp over the entire range 1≤q≤4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.     

Propagating vibrational excitations in molecular chains

We investigate quantum dynamics of vibrational excitations in one-dimensional (1D) molecular chain. Our model includes nearest neighbor interaction between identical molecular sites and one impurity atom placed in the middle (n = 0). We show that upon exciting the impurity site, its excess energy for relatively long for molecular scales time up to 100 ps is not redistributed uniformly among all other degrees of freedom. On the contrary an excitation propagates along the chain, reflected from the chain ends, and quantum interference of these waves yields to recurrence cycles and echo phenomena. For a critical cycle number k _c , echo components of the neighboring cycles start to overlap, and eventually for k ≫ k _c dynamics looks like chaotic one. The critical cycle number k _c depends on the coupling strength 0 ≤ C ≤ 1 of the impurity site with its neighbors n = ±1. k _c achieves the maximum for C ² = 1/2. Our results are in qualitative agreement with experimental data on vibrational excitations in various (CH₂) _n molecular chains, and besides offer a way for loss-free energy transfer between separated in space reaction centers.     

Integrability ofSU(N) spin chains with elliptic exchange

For some one-parameter setH _N of linear combinations ofN(N−1)/2 elementary transpositions {P _jk} (1≤j<k≤N) at arbitrary naturalN≥3 one can construct a variety {I _m} (3≤m≤N) of operators which commute withH _N. Being applied toSU(n) spin representations of the permutation group, this proves the integrability of 1D periodic spin chains with elliptic short-range interaction. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

TDPAC studies of the intercalation compound Li x TiS2 in the region 0≤x≤1

The electrochemical intercalation of Li⁺ into hafnium-doped TiS₂ was studied using time-differential perturbed angular correlations (TDPAC). The¹⁸¹Ta nuclear quadrupole interaction was monitored as a function of the charge transfer,n _F. For low uptakes, 0≤n _F≤0.03, a two-phase region was found with an empty host interaction, characterized byV _q=458(4) MHz, η=0.19(3) and δ-0.083(5), and a second interaction corresponding to lithiated material withv _q=597(5) MHz, η=0.13(4) and δ=0.061(5). No evidence was found for intermediate phases.     

Amorphous-to-crystalline transition in Ge22Se78−x Bi x system

Summary Crystallization kinetics is studied in glassy Ge₂₂Se_78−x Bi _x (0≤x≤10) using isothermal annealing at various temperatures between the glass transition and melting. D.c. conductivity is taken as a parameter to estimate the extent of crystallization (α). The activation energy of crystallization (ΔE) and the order parameter (n) are calculated by fitting the values of α in Avrami’s equations of isothermal transformation. The results indicate that ΔE is highly composition dependent and decreases as the Bi concentration increases.     

Real-gas properties of n-alkanes, O2, N2, H2O, CO, CO2, and H2 for diesel engine operation conditions

The objective of the research outlined in this paper was to develop the analytical approximations for calculating real-gas properties (p-v-T data, thermodynamic functions: internal energy, enthalpy, and entropy, and specific heats) of vapor-phase n-alkanes from C₁ (methane) to C₁₄ (normal tetradecane), O₂, N₂, H₂O, CO, CO₂, and H₂ within the range of pressure 0.05 MPa ≤ p ≤ 20 MPa and temperature 280 K ≤ T ≤ 3000 K aimed for implementation into computational fluid dynamics (CFD)-codes simulating the operation process in modern Diesel engines. The analytical approximations have been developed based on available literature data and on the new equation of state for moderately dense gases. The approximations reported are rather simple and therefore can be used directly in CFD codes. Approximations for mixing rules are also provided.     

Calculation of spectroscopic constants and radiative parameters for A1Σ u+ -X1Σ g+ and B1Πu-X1Σ g+ electronic transitions of sodium dimer

Vibrational, rotational, and centrifugal spectroscopic constants and radiative parameters, i.e., the Einstein coefficients, oscillator strengths, and wave numbers for vibrational transitions in electronic systems of bands A ¹Σ _u ⁺-X ¹Σ _g ⁺ (0 ≤ v′ ≤ 25; 0 ≤ v″ ≤ 44), B ¹Π _u -X ¹Σ _g ⁺ (0 ≤ v′ ≤ 29; 0 ≤ v″ ≤ 47), and the radiative lifetimes for the vibrational levels of excited states of the sodium dimer, are calculated. The calculations are carried out based on semiempirical potential curves constructed in this study. The calculated spectroscopic constants and radiative lifetimes are compared to the experimental values.     

Exciton absorption spectra of Cs<Subscript>2</Subscript>CdI<Subscript>4</Subscript> and Rb<Subscript>2</Subscript>CdI<Subscript>4</Subscript> ferroelastic solid solutions

The exciton absorption spectra of thin films of (Cs_{1 − x} Rb _x )₂CdI₄ solid solutions have been investigated and the refractive index n(λ) in their transparency window in the concentration range of 0 ≤ x ≤ 1 has been measured. The exciton-band parameters and optical permittivity ɛ_∞(x) have been found to linearly depend on the concentration. It is established that excitons are incorporated into the CdI₂ sublattice of the solid solutions and belong to intermediate-coupling ones. The characteristics of excitons in ferroelastics are compared with the corresponding parameters for CdI₂, RbI, and CsI, which are used as components to synthesize ternary compounds.     

Conformal Radii for Conformal Loop Ensembles

The conformal loop ensembles CLE _κ , defined for 8/3 ≤ κ ≤ 8, are random collections of loops in a planar domain which are conjectured scaling limits of the O(n) loop models. We calculate the distribution of the conformal radii of the nested loops surrounding a deterministic point. Our results agree with predictions made by Cardy and Ziff and by Kenyon and Wilson for the O(n) model. We also compute the expectation dimension of the CLE _κ gasket, which consists of points not surrounded by any loop, to be

Moments and Distributions of Trajectories in Slow Random Monads

Given a finite set B (basin) with n>1 elements, which we call points, and a map M:B→B, we call such pairs (B,M) monads. Here we study a class of random monads, where the values of M(⋅) are independently distributed in B as follows: for all a,b∈B the probability of M(a)=a is s and the probability of M(a)=b, where a≠b, is (1−s)/(n−1). Here s is a parameter, 0≤s≤1. We fix a point ⊙∈B and consider the sequence M ^t (⊙), t=0,1,2,… . A point is called visited if it coincides with at least one term of this sequence. A visited point is called recurrent if it appears in this sequence at least twice; if a visited point appears in this sequence only once, it is called transient. We denote by Vis _n , Rec _n and Tra _n the numbers of visited, recurrent and transient points respectively. We prove that, when n tends to infinity, Vis _n and Tra _n converge in law to geometric distributions and Rec _n converges in law to a distribution concentrated at its lowest value, which is one. Now about moments. The case s=1 is trivial, so let 0≤s<1. For any natural number k there is a number such that the k-th moments of Vis _n , Rec _n and Tra _n do not exceed this number for all n. About Vis _n : for any natural k the k-th moment of Vis _n is an increasing function of n. So it has a limit when n→∞ and for all n it is less than this limit. About Rec _n : for any k the k-th moment of Rec _n tends to one when n tends to infinity. About Tra _n : for any k the k-th moment of Tra _n has a limit when n tends to infinity.     

Muon diffusion in β-V2H

Hydrogen diffusion in the ordered hydride β-V₂H is mainly brought about by a minority fraction of interstitial atoms on antistructural sites. Recently, this mechanism was elucidated in a single crystal QNS study at temperatures close to the critical point (390 K≤T≤440 K) where already an appreciable amount of antistructural sites is occupied. Here we use the positive muon as a radioactive hydrogen tracer in order to show that the same diffusion mechanism is also valid at low temperatures (80 K≤T≤320 K) where the different jump processes are very slow and where the fraction of antistructural atoms is tiny but nevertheless dominates the long range diffusion.     

Dispersion of the Voigt effect in the magnetic semiconductors Cd1−x MnxTe

Spectral measurements of the Voigt birefringence Δn were performed for the cubic magnetic semiconductor Cd_1−x Mn _x Te (0≤x≤0.52) in order to investigate how the exchange interaction of Mn²⁺ ions with itinerant electrons depends on the electron wave vector. It was determined that Δn/x ² is independent of x and the magnetic field direction, i.e., the effect is due to the Mn²⁺ ions and is isotropic. Below the band gap edge the dispersion of the birefringence Δn can be described well in all samples by the unusual dependence Δn∼(E _g −ℏω) ^−3.5. This can be explained by a decrease of the exchange interaction of Mn²⁺ ions with itinerant electrons with increasing distance from the center of the Brillouin zone. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 569–573 (25 April 1998)     

Quantum oscillations of the resistivity and hall coefficient and the quantum limit in Bi<Subscript>0.93</Subscript>Sb<Subscript>0.07</Subscript> alloys in a magnetic field along the trigonal axis

The dependences of the electrical resistivity ρ and the Hall coefficient R on the magnetic field have been measured for single-crystal samples of the n-Bi_0.93Sb_0.07 semiconductor alloys with electron concentrations in the range 1 × 10¹⁶ cm⁻³ < n < 2 × 10¹⁸ cm⁻³. It has been found that the measured dependences exhibit Shubnikov-de Haas quantum oscillations. The magnetic fields corresponding to the maxima of the quantum oscillations of the electrical resistivity are in good agreement with the calculated values of the magnetic fields in which the Landau quantum level with the number N intersects the Fermi level. The quantum oscillations of the Hall coefficient with small numbers are characterized by a significant spin splitting. In a magnetic field directed along the trigonal axis, the quantum oscillations of the resistivity ρ and the Hall coefficient R are associated with electrons of the three-valley semiconductor and are in phase with the magnetic field. In the case of a magnetic field directed parallel to the binary axis, the quantum oscillations associated both with electrons of the secondary ellipsoids in weaker magnetic fields and with electrons of the main ellipsoid in strong magnetic fields (after the overflow of electrons from the secondary ellipsoids to the main ellipsoid) are also in phase. In magnetic fields of the quantum limit ħω _c /2 ≥ E _F, the electrical conductivity increases with an increase in the magnetic field: σ₂₂(H) ∼ H ^k . A theoretical evaluation of the exponent in this expression for a nonparabolic semiconductor leads to values of k close to the experimental values in the range 4 ≤ k ≤ 4.6, which were obtained for samples of the semiconductor alloys with different electron concentrations. A further increase in the magnetic field results in a decrease of the exponent k and in the transition to the inequality σ₂₂(H) ≤ σ₂₁(H).     

The Effect of the Number of Simulations on the Exponents Obtained by Finite-Size Scaling Relations of the Order Parameter and the Magnetic Susceptibility for the Four-Dimensional Ising Model on the Creutz Cellular Automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton using finite-size lattices with linear dimension 4≤L≤8. The exponents in the finite-size scaling relations for the order parameter and the magnetic susceptibility at the finite-lattice critical temperature are computed to be β=0.49(7), β=0.49(5), β=0.50(1) and γ=1.04(4), γ=1.03(4), γ=1.02(4) for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are consistent with the renormalization group predictions of β=0.5 and γ=1. The values for the critical temperature of the infinite lattice T _c (∞)=6.6788(65), T _c (∞)=6.6798(69), T _c (∞)=6.6802(70) are obtained from the straight-line fit of the magnetic susceptibility maxima using 4≤L≤8 for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are in very good agreement with the series expansion results of T _c (∞)=6.6817(15), T _c (∞)=6.6802(2), the dynamic Monte Carlo result of T _c (∞)=6.6803(1), the cluster Monte Carlo result of T _c (∞)=6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm result of T _c (∞)=6.6802632±5×10⁻⁵.