Monte Carlo optimisation of correlated wave functions for normal two-electron systems

A simple, new type of correlated wave function is proposed for the studies of normal two-electron atomic systems: ψ(r₁, r₂) = Σc_mΦ_m(r₁, r₂) with Φ_m(r₁, r₂) = exp[−(r₁ + r₂)]/(br₁₂ + a)^m, where , a, b are non-linear variational parameters. A notable feature of this basis function is that only three terms are required within the framework of the Raleigh-Ritz variational principle to obtain fairly accurate energy eigenvalues and satisfactory cusp conditions. The non-linear variational parameters are optimised by using the Monte Carlo technique.     

A model for the size distribution of customer groups and businesses

We present a generalization of the dynamical model of information transmission and herd behavior proposed by Eguíluz and Zimmermann. A characteristic size of group of agents s₀ is introduced. The fragmentation and coagulation rates of groups of agents are assumed to depend on the size of the group. We present results of numerical simulations and mean field analysis. It is found that the size distribution of groups of agents n_s exhibits two distinct scaling behavior depending on ss₀ or s>s₀. For ss₀, n_ss^−(5/2+δ), while for s>s₀,n_ss^{−(5/2−δ)}, where δ is a model parameter representing the sensitivity of the fragmentation and coagulation rates to the size of the group. Our model thus gives a tunable exponent for the size distribution together with two scaling regimes separated by a characteristic size s₀. Suitably interpreted, our model can be used to represent the formation of groups of customers for certain products produced by manufacturers. This, in turn, leads to a distribution in the size of businesses. The characteristic size s₀, in this context, represents the size of a business for which the customer group becomes too large to be kept happy but too small for the business to become a brand name.     

准周期层状铁磁超晶格的实空间重整化群方法

本文用实空间重整化群方法讨论了准周期层状铁磁超晶格的磁自旋波,用Reduce语言推导了decimation变换公式,从而求得了局域格林函数、局域态密度和约化磁矩。发现局域态密度的带宽和约化磁矩与最近邻相互作用J₁、J₂及格点自旋s_a、s_b密切相关。     

Effects of the dust size distribution in one-dimensional quantum dusty plasma

The effects of the dust size distribution in ultracold quantum dusty plasmas are investigated. The amplitude φ_m and width ω of quantum dust acoustic waves are studied with different dust size distributions in the system. The φ_m and ω of the quantum dust acoustic waves are found to increase as the total number density increases. The φ_m and ω are greater for unusual dusty plasmas than for typical dusty plasmas. Moreover, as the Fermi temperature of the dust grains increases, the φ_m of the wave decreases. The ω of quantum dust acoustic waves increases as the speed u₀ of the wave increases.     

稠苯芳杂环及其烷基质子化学位移的计算

本文提出了予测稠苯芳杂环及其烷基链上质子化学位移的计算方法。 将稠苯芳杂环化合物用凯库勒式表示,计算式为为需考虑的苯环内的乙烯基效应。σ_mi,ci为各苯环的环流效应。σ_1,Hc为各芳杂环的屏蔽效应,对杂环上质子它就是该单独芳杂环上相应质子的δ值,对苯环上质子要将它分解为各结构因素的效应,即:σ_1,He=(1/2)^d-1δ_x=y(或σ_z)+σ_c-c·σ_m,H. σ_x-y与σ_z为杂原子或其基团的屏蔽效应,σ_c=c为存在于芳杂环中的乙烯基的效应,σ_m,Hc为芳杂环的环流效应,d为对不同质子所考虑的键数。有取代基时需考虑取代基的效应。计算环上烷基质子的公式为:δ=σ_p,CH3+ασ_c,CH3+βσ_t,CH3+σ_l,G σ_l,G为稠苯芳杂环基的某级效应。     

A spectroscopic ellipsometric investigation of new critical points of Zn1−xMnxS epilayers

Zn_1−xMn_xS epilayers were grown on GaAs (1 0 0) substrates by hot-wall epitaxy. X-ray diffraction (XRD) patterns revealed that all the epilayers have a zincblende structure. The optical properties were investigated using spectroscopic ellipsometry at 300 K from 3.0 to 8.5 eV. The obtained data were analyzed for determining the critical points of pseudodielectric function spectra, (E) = ₁(E) + i₂(E), such as E₀, E₀ + Δ₀, and E₁, and three E₂ (Σ, Δ, Γ) structures at a lower Mn composition range. These critical points were determined by analytical line-shapes fitted to numerically calculated derivatives of their pseudodielectric functions. The observation of new peaks, as well as the shifting and broadening of the critical points of Zn_1−xMn_xS epilayers, were investigated as a function of Mn composition by ellipsometric measurements for the first time. The characteristics of the peaks changed with increasing Mn composition. In particular, four new peaks were observed between 4.0 and 8.0 eV for Zn_1−xMn_xS epilayers, and their characteristics were investigated in this study.     

27Al NMR study in ZrNiAl

We have studied the microscopic properties of the hexagonal ZrNiAl, a model compound for a wide family of intermetallic compounds crystallizing in this type of structure, by using ²⁷Al NMR spectroscopy. We have investigated the lineshape of static and MAS NMR spectra as a function of magnetic field strength (4.7–9.4 T) and temperature (5–300 K). Our data indicate that the ²⁷Al NMR spectra result from a combined effect of quadrupole and anisotropic shift interactions. The ²⁷Al nuclei are in an environment characterized by the quadrupole coupling constant e²qQ/h of 3.3 MHz, asymmetry parameter η_Q of 0.42, isotropic shift δ_iso of 393 ppm, shift anisotropy δ_anis = δ_zz − (δ_xx + δ_yy)/2 of 150 ppm, and asymmetry factor η_S of 0.5. They are found to be temperature independent. The spin–lattice relaxation rate measured at 7.05 T is proportional to the temperature with T₁T = 135 s K. The mechanisms responsible for observed values of δ_iso, δ_anis, T₁T, and the enhanced Korringa constant are discussed.     

Crosstalk between two-photon and two-color (two-photon) excitation in optical beam induced current generation with two confocal excitation beams

We analyze the influence of residual two-photon excitation (2PE) in two-color (two-photon) optical beam induced current (2CE-OBIC) generation in wide band gap semiconductor samples. 2CE-OBIC generation is accomplished with two confocal excitation beams of separation angle θ and wavelengths λ₁ and λ₂ where , λ_e = hc/E_b, h is the Planck’s constant, c is speed of light in vacuum, and E_b is the energy band gap. Because the conduction band of the sample is a continuum, at least one excitation beam would also contribute an undesirable 2PE-OBIC signal that degrades the signal-to-noise ratio of the measured 2CE-OBIC response and broadens the effective OBIC distribution in the sample particularly when θ ≠ 0 or π. We show that the deleterious effects of crosstalk are reduced by a careful selection of λ₁ and λ₂ and the relative excitation beam intensities. λ₁ and λ₂ should be chosen to minimize the ratio of the two-photon absorption coefficients (β₁, β₂) to the 2CE absorption coefficient β₁₂ or at least satisfy the constraint: β₁ + β₂  β₁₂. Keeping the two excitation intensities equal is beneficial only when β₁ = β₂. Otherwise, it is advantageous to bias the intensity ratio towards the wavelength with a lower 2PE absorption coefficient.     

Superconductivity and pseudogap states studied by microwave conductivity measurements of λ-(BEDT-TSF)2GaCl4

We have investigated the microwave response at 45 GHz in an organic superconductor λ-(BEDT-TSF)₂GaCl₄ with T_c = 4.8 K. We determine the μ₀H_c2–T phase diagram from microwave loss and find that the superconducting state is in the pure limit (l/ξ_GL  10). Although the real part of the complex conductivity (=σ₁ + iσ₂) does not show a coherence peak just below T_c, the London penetration depth completely saturates at low temperatures down to T/T_c = 0.2, which may provide an evidence for a conventional s-wave pairing. In the metallic state below about 50 K, (parallel to the c-axis) deviates downward from , while σ₂, which should be zero in a conventional metal, increases exponentially toward T_c. In spite of the fact that the Hagen–Rubens limit is well satisfied as far as the dc conductivity is concerned, a Drude model is unable to explain the large positive σ₂. In order to explain such anomalies in the metallic state, we propose a possible existence of so-called a pseudogap near a Fermi level. The anomalous increase of the positive σ₂ may be attributed to an appearance of pre-formed electron pairs in the pseudogap state. This appearance can be regarded as a precursor to the superconducting transition. Such a precursory phenomenon has been observed also in the isostructural FeCl₄ salt with the anomalous metallic states, which shows a negative σ₂ in contrast to the GaCl₄ salt. Just the opposite of ground states in between the GaCl₄ and FeCl₄ salts may result in the contrasting anomalous metallic states with different precursory phenomena with opposite signs of σ₂.     

Molecular parameters describing intermolecular interactions in the electrooptical Kerr effect

Electrooptical Kerr effect has been studied in binary solutions of a dipolar liquid (-picoline, β-picoline) in a non-dipolar solvent (benzene, p-xylene) and 1,4-dioxane in the full range of concentrations of the dipolar component (0 ≤ f₂ ≤ 1). The experimental Kerr constant K_s of the solutions, refraction index n_s, density ρ_s and the dielectric constant ε_s have been measured and used for the calculation of the molar Kerr constants K_S^M within the Onsager local field model. Analysis of changes in the molar Kerr constants as a function of the solute concentration by fits of theoretical functions to the experimental ones has permitted a determination of the parameters characterizing intermolecular interactions in binary solutions.     

Nonlinear refractive index measurements in antimony–sulfide glass films using a single beam nonlinear image technique

The nonlinear refractive index, n₂, of films based on the new glass system Sb₂O₃–Sb₂S₃ was measured at 1064 nm with laser pulses of 15 ps, using a single-beam nonlinear image technique in presence of a phase object. The films were prepared from bulk glasses by RF-sputtering. A large value of n₂ = 3 × 10⁻¹⁵ m²/W, which is three orders of magnitude larger than for CS₂, was determined. The result shows the strong potential of antimony–sulfide glass films for integrated nonlinear optics.     

Distance functions and statistics

This paper proves that the Riemannian distance function is maximal in the class of distance functions associated with the Riemannian metric tensor.

Secondly, it is proven that there exists a unique minimum of

on a complete Riemannian surface (M,g) with small curvature, small curvature change and injectivity radius +∞. Here p_iM and γ_v is the maximal geodesic with initial velocity v and 0<t₁<<t_m.     

Redshift drift constraints on f(T) gravity

We explore the impact of the Sandage−Loeb (SL) test on the precision of cosmological constraints for f(T) gravity theories. The SL test is an important supplement to current cosmological observations because it measures the redshift drift in the Lyman-α forest in the spectra of distant quasars, covering the “redshift desert” of 2≲z≲5. To avoid data inconsistency, we use the best-fit models based on current combined observational data as fiducial models to simulate 30 mock SL test data. We quantify the impact of these SL test data on parameter estimation for f(T) gravity theories. Two typical f(T) models are considered, the power-law model f(T)_PL and the exponential-form model f(T)_EXP. The results show that the SL test can effectively break the existing strong degeneracy between the present-day matter density Ω_m and the Hubble constant H₀ in other cosmological observations. For the considered f(T) models, a 30-year observation of the SL test can improve the constraint precision of Ω_m and H₀ enormously but cannot effectively improve the constraint precision of the model parameters.     

Possible phase transition of anisotropic frustrated Heisenberg model at finite temperature

The frustrated spin-1/2 J_1a–J_1b–J₂ antiferromagnet with anisotropy on the two-dimensional square lattice was investigated, where the parameters J_1aand J_1b represent the nearest neighbor exchanges and along the x and y directions, respectively. J₂ represents the next-nearest neighbor exchange. The anisotropy includes the spatial and exchange anisotropies. Using the double-time Green’s function method, the effects of the interplay of exchanges and anisotropy on the possible phase transition of the Néel state and stripe state were discussed. Our results indicated that, in the case of anisotropic parameter 0≤η<1, the Néel and stripe states can exist and have the same critical temperature as long as J₂ = J_1b/2. Under such parameters, a first-order phase transformation between the Néel and stripe states can occur below the critical point. For J₂ ≠J_1b/2, our results indicate that the Néel and stripe states can also exist, while their critical temperatures differ. When J₂>J_1b/2, a first-order phase transformation between the two states may also occur. However, for J₂<J_1b/2, the Néel state is always more stable than the stripe state.     

Some properties of the spectral flow in semiriemannian geometry

Let be the action integral on a semiriemannian manifold ( , g) defined on the space of the curves z : [0, 1] → joining two given points z₀ and z₁. The critical points of ƒ are the geodesics joining z₀ and z₁. Let s ε [0, 1]. We study the behavior, in dependence of s, of the eigenvalues of the Hessian form of ƒ evaluated at z, restricted to the interval [0, s]. A formula for the derivative of the eigenvalues is given and some applications are shown.     

Phase transitions in the superionic protonic conductor CsHSeO4 investigated by Brillouin spectroscopy

A Brillouin investigation in CsHSeO₄ has been performed over the temperature range 20–165 °C which includes two phase transitions, in particular the transition to the superionic phase near T_s = 129 °C. We observed strong discontinuities for elastic constants C₁₁, C₂₂ and C₃₃ at T_s and a broadening of the Brillouin lines above T_s. The results are discussed on the basis of a linear coupling between strains and mobile protons.     

Electrostatic stiffness properties of charged bilayers

We calculate the exact stiffness constants χ, , c₀ of mean, Gaussian, and spontaneous curvature for a double layer of surface charges separated by a fixed distance 2d in an electrolyte with finite screening length l₀. This extends earlier studies of the limits of very small and very large d/l_D.     

Temporary phase segregation processes during the oxidation of (Fe0.7Mn0.3)0.99O in N2---H2O atmosphere

A two-step thermochemical cycle with the ternary metal oxide system (Fe_{1 − x}Mn_x)₃O₄/(Fe_{1 − x}Mn_x)_{1 − y}O is applied to convert solar energy to chemical energy. Experimental investigations on the water splitting reaction of (Fe_{1 − x}Mn_x)_{1 − y}O revealed temporary formation of a manganese rich rock salt phase and an iron rich spinel phase due to phase segregation processes.     

Diamagnetic impurity effects on the Néel temperature in La2CuO4 and related materials

To investigate why the sensitivity of the Néel temperature T_N of the antiferromagnetic (AF) layered copper perovskites (typically La₂CuO₄) to diamagnetic impurities such as Zn is reportedly much larger than in the AF members of the K₂NiF₄ family, we first treat the effect of a concentration c of impurities on the uncorrelated electronic states in the coherent potential approximation (CPA). Then we consider the Heisenberg hamiltonian as the large correlation limit of the Hubbard hamiltonian for a single band of impurity-modified electronic states. The correlation effects are treated variationally. The model is solved explicity by using a rectangular density of states, and we obtain the c-dependent exchange J, staggered moment S_q, spin wave velocity and transverse susceptibility at zero temperature. We take into consideration several recently proposed formulae for T_N in the clean limit, and include the impurity effects by exploiting the results obtained, in order to test their predictions against the experimental T_N(c) data for La₂Cu_1−cZn_cO₄. Our results suggest that, to explain the difference between the K₂NiF₄ and the La₂ CuO₄ families, one should consider both the sign and the magnitude of the difference I≡ε^B−ε^A between impurity (B) and host (A) ionic potentials. The slowly decreasing trend of T_N(c) in the K₂NiF₄ family is reproduced if I is negative and sizeable, or positive but very small, while the quick decrease typical of the copper perovskites requires a positive and rather large I. For reasonable values of the interaction parameters, among the several models we compare, only the model of Chakravarty, Halperin and Nelson is able to semi-quantitatively reproduce the non-linear behaviour of T_N(c) reported for La₂Cu_1−cZn_cO₄, provided the spin stiffness is assumed to scale with c as appropriate to Fermi liquids.