Effect of Fe substitution on the thermal expansion of the highT c superconductor Y1Ba2Cu3O y

Thermal expansion measurements have been carried out on Fe substituted superconducting compounds Y₁Ba₂(Cu_1−x Fe _x )₃O _y (0<x<4%) using a high resolution dilatometer employing the three terminal capacitance technique. The experimental set up is sensitive enough to detect changes in α of less than 10⁻⁸K⁻¹. Results show that the jump Δα in the coefficient of linear thermal expansion at the superconducting transition temperature,T _c, increases almost linearly with Fe concentration. The normal state thermal expansion coefficient α first decreases, attains a minimum value aroundx=1% and then increases for higher Fe concentrations. The oxygen content per unit formula is almost constant up tox=1% and then increases rapidly withx. It has also been observed that the anomalous behaviour of α around 260 K observed by Meingastet al [22] for Fe concentrationx=5% is due to inadequate annealing of the sample.     

Time Quasi-Periodic Unbounded Perturbations¶of Schrödinger Operators and KAM Methods

We eliminate by KAM methods the time dependence in a class of linear differential equations in ℓ² subject to an unbounded, quasi-periodic forcing. This entails the pure-point nature of the Floquet spectrum of the operator H ₀+εP(ωt) for ε small. Here H ₀ is the one-dimensional Schr?dinger operator p ²+V, V(x)∼|x|^α, α <2 for |x|→∞, the time quasi-periodic perturbation P may grow as |x|^β, β <(α−2)/2, and the frequency vector ω is non resonant. The proof extends to infinite dimensional spaces the result valid for quasiperiodically forced linear differential equations and is based on Kuksin's estimate of solutions of homological equations with non-constant coefficients. Received: 3 October 2000 / Accepted: 20 December 2000     

Clustering of exponentially separating trajectories

It might be expected that trajectories of a dynamical system which has no negative Lyapunov exponent (implying exponential growth of small separations) will not cluster together. However, clustering can occur such that the density ρ(Δx) of trajectories within distance |Δx| of a reference trajectory has a power-law divergence, so that ρ(Δx) ∼ |Δx| ^−β when |Δx| is sufficiently small, for some 0 < β < 1. We demonstrate this effect using a random map in one dimension. We find no evidence for this effect in the chaotic logistic map, and argue that the effect is harder to observe in deterministic maps.     

Capacitance-voltage behaviour inp-type ɛ-GaSe single crystal ∥c at different temperatures

Summary  Capacitance-voltage measurements have been carried out onp-type ɛ-GaSe single crystal ∥c in the temperature range 300 to 360 K, with applied voltages of -1, 0 and +1 V. TheC-V measurements in this temperature range have shown a shift in capacitanceC and conductanceG to the higher values with an increase in temperature. The depletion layer widthW, the Debye length L_D and the doping densityN _α have been worked out and plots ofN _α vs. W have shown a decrease inW with an increase in temperature. The plots of L_D vs. N _α vary as 1/N_α^1/2, which gives N_αL_D ⋍ 3.3 × 10¹¹ charges/m² for doping density of 10¹⁶m⁻³. The values ofG at different temperatures have been used to obtain the activation energies, which are found to be ΔE ⋍ 0.11 eV for -1 and +1 V applied voltages, and ΔE ⋍ 0.06 eV for zero volt. The authors of this paper have agreed to not receive the proofs for correction.     

X-ray emission studies of evolution of the electron and spin structures of Mn in mixed manganites Ln1 ? xSrxMnO3 (Ln = La, Sm, and Ce)

The chemical shift DE_Kb1 \Delta E_{K_{\beta 1} } and the exchange splitting ΔE _split of the emission X-ray Mn K _β1 line in mixed manganites Ln _{1 − x} Sr _x MnO₃ (Ln = La, Sm, and Ce) have been systematically studied for the first time. It has been found that DE_Kb1 \Delta E_{K_{\beta 1} } and ΔE _split are almost the same in the range x < 0.4–0.5, as is the case in Mn₂O₃, and then they decrease relatively quickly to the values characteristic of MnO₂. It has been assumed that such a behavior corresponds to the model where in the region of hole doping (x < 0.5), the ground state is a mixture of configurations Mn³⁺ 3d ⁴ and $3d^4 \underset{\raise0.3em\hbox{$3d^4 \underset{\raise0.3em\hbox{, so that the second configuration fraction increases with x. At high values of x, the configuration Mn⁴⁺ 3d ³ should be taken into account; the contribution of this configuration increases with increasing degree of doping, and it becomes dominant at x = 1. In all cases, the manganese state is high-spin.     

Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L _x, L _y) is assumed to be 2Δ^-2θ(L _x - 1/3 + Δ/3)θ(L _y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L _x - L _y), where θ( ^{. . .} ) is the Heaviside function, Δ is the shape variance and L_i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α ∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ⁽³⁾ _e|/χ⁽³⁾ ₁ exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ⁽³⁾ _e|/χ⁽³⁾ ₁ on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does. Received 10 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: lgaophys@pub.sz.jsinfo.net     

Fractal differential equations and fractal-time dynamical systems

Differential equations and maps are the most frequently studied examples of dynamical systems and may be considered as continuous and discrete time-evolution processes respectively. The processes in which time evolution takes place on Cantor-like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation of these systems requires an appropriate framework. A new calculus calledF ^α-calculus, is a natural calculus on subsetsF⊂ R of dimension α,0 < α ≤ 1. It involves integral and derivative of order α, calledF ^α-integral andF ^α-derivative respectively. TheF ^α-integral is suitable for integrating functions with fractal support of dimension α, while theF ^α-derivative enables us to differentiate functions like the Cantor staircase. The functions like the Cantor staircase function occur naturally as solutions ofF ^α-differential equations. Hence the latter can be used to model fractal-time processes or sublinear dynamical systems. We discuss construction and solutions of some fractal differential equations of the form

Crystal structure and electrical properties of GdxMn1 ? xS and TixMn1 ? xSe solid solutions

Regions of the existence of sulfide Gd _x Mn_{1 − x} S and selenide Ti _x Mn_{1 − x} Se solid solutions have been identified. Their electrical and thermoelectric properties have been studied in the temperature range 80–900 K. It has been established that the substitution of Gd²⁺ and Ti²⁺ ions for Mn²⁺ cations initiates reversal of the type of charge carrier with respect to the starting compounds MnS and MnSe. The cation substitution in solid solutions brings about a change from the hole conduction (α > 0) characteristic of the manganese monosulfide and monoselenide to the electronic conduction (α < 0).     

Adsorption of a semiflexible wormlike chain

Adsorption of ideal polymers with stiff backbone onto a flat surface is considered theoretically. Both scaling approach and quantitative theory are developed. We predict a self-similar monomer concentration profile c(x) ∼ x ^-4/3 near the surface (when the distance to the surface x is much smaller than the chain persistence length l /2). The typical conformation of a weakly adsorbed chain can be viewed as a sequence of alternating flat (2-dimensional) trains of wormlike short loops (flat blobs) and coil-like (3-dimensional) loops forming a triple-layer structure: contact layer (x < Δ) of adsorbed fragments virtually laid on the surface, proximal layer (Δ < x < l) of flat blobs, and more dilute distal corona layer (x > l). Here Δ defines the range of monomer/surface attraction, Δ ≪ l. The adsorption transition is continuous. However, its relative width is small (T ^* is the adsorption temperature, ΔT is the relevant temperature interval): ∼ , i.e. a discontinuous transition in the limit Δ/l↦ 0. Received 10 October 2002 and Received in final form 22 November 2002 RID="a" ID="a"Permanent address: Physics Department, Moscow State University, Moscow 119992, Russia. e-mail: semenov@polly.phys.msu.ru     

Dielectric properties of perovskite ceramics of (1–x)BiFeO3 ? x(KBi)1/2TiO3 (0.40 < x < 0.85) solid solutions from impedance spectroscopy data

The dielectric properties of the ceramics of (1 − x)BiFeO₃ − x(KBi)_1/2TiO₃ (0.40 < x < 0.85) solid solutions with an orthorhombic structure have been studied using impedance spectroscopy in the frequency range 25–10⁶ Hz at different temperatures. It has been shown that these solid solutions undergo a diffuse ferroelectric phase transition. The Curie temperature is found to be in the range 620–640 K. The activation energies of dielectric polarization relaxation (δE _M ) and dc charge carriers (ΔE _dc) are determined. It has been established that, in the vicinity of 460 K, ΔE _dc increases jumpwise as the temperature increases.     

On the mechanism of phase transformation in Ag2Se

A differential thermal analysis ΔT _y (T) in vacuum has been performed, and the temperature gradient ΔT _x (T) along the Ag₂Se sample during the transition α → β has been studied. It has been shown that the transitions α → α′ and β′ → β are displacive transitions and that the transition α′ → β′ is a reconstructive transition. It has been found that the temperature gradient along the sample during the transition α′ → β′ passes through a deep minimum due to a strong increase in the specific heat capacity.     

Josephson and single-particle currents between partially dielectricized superconductors with charge-density waves

The amplitudes of the nonstationary Josephson current I ¹, the interference current I ², and the quasiparticle current J through symmetric and asymmetric tunnel junctions, including superconductors with charge density waves, are calculated. In the symmetric (s) case the dependence of the Josephson current I _s ¹ on the voltage V on the junction has a logarithmic singularity at |eV|=2Δ, Δ+D, and 2D, where , Δ and Σ are the superconducting and dielectric order parameters, and e is the unit charge. At temperatures T≠0 jumps appear in the current-voltage characteristics I _s ¹ (V) at |eV|=D−Δ. Jumps and singularities are observed in the currents I _s ² and J _s at the same voltages at which singularities and jumps appear in I _s ¹ , respectively. In the nonsymmetric (ns) junctions which include an ordinary superconductor, singularities and jumps occur at |eV|=D+Δ_BCS, Δ+Δ_BCS, and (for T≠0) |D−Δ_BCS| and |Δ−Δ_BCS|, where Δ_BCS is the order parameter of an ordinary superconductor. The quasiparticle current J _ns is an asymmetric function of the voltage V and does not depend on the sign of Σ. The results are compared with experiment. Fiz. Tverd. Tela (St. Petersburg) 39, 991–999 (June 1997)     

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)     

Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order <Emphasis Type="Italic">α</Emphasis>

In a first stage, the paper deals with the derivation and the solution of the equation of the probability density function of a stochastic system driven simultaneously by a fractional Gaussian white noise and a fractional Poissonian white noise both of the same order. The key is the Taylor’s series of fractional order f(x + h) = E _α(h^αD _x ^α)f(x) where E _α() denotes the Mittag-Leffler function, and D _x ^α is the so-called modified Riemann-Liouville fractional derivative which removes the effects of the non-zero initial value of the function under consideration. The corresponding fractional linear partial differential equation is solved by using a suitable extension of the Lagrange’s technique involving an auxiliary set of fractional differential equations. As an example, one considers a half-oscillator of fractional order driven by a fractional Poissonian noise.      

Correlation between the electric-field effect and weak-link type in YBa2Cu3−x Oy and YBa2Cu3−x Oy /Agx high-T c superconducting ceramics

An experimental study is reported of the effect of an electric field E⩽120 MV/m and of temperature T on the critical current I _c and I-V characteristics of yttrium-based high-T _c superconducting ceramics. The materials studied were copper-deficient ceramics, YBa₂Cu_3−x O_y (D samples), and YBa₂Cu_3−x O_y/Ag_x ceramics [S samples with silver present in amounts equal to the copper deficiency (0⩽x⩽0.4)]. It has been established that in D samples at 77 K, the electric field increases I _c and reduces substantially R for I>I _c, whereas in S samples no field effect is observed. Measurements of the I _c(T) dependence near the critical temperature showed that they can be described for all samples by a relation of the type I _c =const(1−T/T _c )^α, where α≈1 for the D samples, and α≈2 for the S samples. The results obtained suggest that the electric-field effect correlates with the existence in the ceramic of SIS-type weak links at grain boundaries. Fiz. Tverd. Tela (St. Petersburg) 40, 1195–1198 (July 1998)     

Low energy excitations in KMnO4 with 1 eV<=ΔE<=10 eV from electron-energy loss spectroscopy

Electron-energy loss spectra of potassium permanganate (KMnO₄) with primary electron energies 25 eV<=E₀<=500 eV show 7 peaks in the energy-loss range 1 eV<=ΔE<=10eV and are successfully analysed with a superposition of 7 independent Gaussians. The intensity of these lines follow roughly a power-law dependence on the primary energy I∝E ₀ ^-α . There are two groups of lines, the first with an exponent α≈0.5, while the lines in the second group decay much stronger with increasingE ₀ corresponding to a value 0.9<=α<=1.3. The 4 lines in the first group are identified as dipole allowed transitions by comparison to recent first principle molecular-orbital calculations for the (MnO₄) molecule by H. Nakai et al. The dipole-allowed excitation spectrum obtained from this analysis agrees very well with these first principle calculations.     

2p3/2?13x?1?3x?13d?1 X-ray satellites spectra in the Lα1 region of 4d transition elements

The X-ray satellite spectra arising due to 2p _3/2 ⁻¹3x ⁻¹−3x ⁻¹3d ⁻¹ (x ≡ s, p, d) transition array, in elements with Z = 40 to 48, have been calculated, using available Hartree-Fock-Slater (HFS) data on 1s ⁻¹−2p ⁻¹ 3x ⁻ and 2p _3/2 ⁻¹−3x ⁻¹,3x ⁻¹ Auger transition energies. The relative intensities of all the possible transitions have been estimated by considering cross — sections for the Auger transitions simultaneous to a hole creation and then distributing statistically the total cross sections for initial two hole states 2p _3/2 ⁻¹−3x ⁻¹ amongst various allowed transitions from these initial states to 3x ⁻¹ 3d ⁻¹ final states by Coster-Kronig (CK) and shake off processes. In both these processes initial single hole creation is the prime phenomenon. Each transition has been assumed to give rise to a Gaussian line and the overall spectrum has been computed as the sum of these Gaussian curves. The calculated spectra have been compared with the measured satellite energies in Lα₁ spectra. Their intense peaks have been identified as the observed satellite lines. The peaks in the theoretical satellite spectra were identified as the experimentally reported satellites α₃, α₄ and α₅, which lie on the high-energy side of the Lα₁ dipole line.     

Superdiffusion and stable laws

The superdiffusion equation with a fractional Laplacian Δ ^α/2 in _N-dimensional space describes the asymptotic (t→∞) behavior of a generalized Poisson process with the range (discontinuity) distribution density ∼|x|−α−1. The solutions of this equation belong to a class of spherically symmetric stable distributions. The main properties of these solutions are given together with their representations in the form of integrals and series and the results of numerical calculations. It is shown that allowance for the finite velocity of free particle motion for α>1 merely amounts to a reduction in the diffusion coefficient with the form of the distribution remaining stable. For α<1 the situation changes radically: the expansion velocity of the diffusion packet exceeds the velocity of free particle motion and the superdiffusion equation becomes physically meaningless. Zh. éksp. Teor. Fiz. 115, 1411–1425 (April 1999)     

Fractal simulation of the resistivity and capacitance of arsenic selenide

The temperature dependences of the ac resistivity R and ac capacitance C of arsenic selenide were measured more than four decades ago [V. I. Kruglov and L. P. Strakhov, in Problems of Solid State Electronics, Vol. 2 (Leningrad Univ., Leningrad, 1968)]. According to these measurements, the frequency dependences are R ∝ ω^{−0.80±0.01} and ΔC ∝ ω^{−0.120±0.006} (ω is the circular frequency and ΔC is measured from the temperature-independent value C ₀). According to fractal-geometry methods, R ∝ ω^1−3/h and ΔC ∝ ω^−2+3/h , where h is the walk dimension of the electric current in arsenic selenide. Comparison of the experimental and theoretical results indicates that the walk dimensions calculated from the frequency dependences of resistivity and capacitance are h _R = 1.67 ± 0.02 and h _C = 1.60 ± 0.08, which are in agreement with each other within the measurement errors. The fractal dimension of the distribution of conducting sections is D = 1/h = 0.6. Since D < 1, the conducting sections are spatially separated and form a Cantor set.