1/f-type fluctuation of electron transmission in one-dimensional disordered systems

A universal feature of 1/f-type fluctuation is numerically observed in the system-size n dependence of the transmission amplitude t_n in various one-dimensional disordered systems. The power spectrum P(f) of the transmission coefficient T(n)=|t_n|² exhibits the power law of 1/f², irrespective to the type of disorder of the system whether it is of short-range or of long-range correlation. That of the phase θ_t(n) of t_n also does the universal power law of 1/f^1.4.     

Projective and affine connections on S and integrable systems

It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L² metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S¹. The space of differential operators Δ⁽ⁿ⁾=∂ⁿ+u₂∂ⁿ⁻²++u_n form the space of extended or generalized projective connections. If a projective connection is factorizable Δ⁽ⁿ⁾=(∂−((n+1)/2−1)p₁)(∂+(n−1)/2p_n) with respect to quasi primary fields p_i’s, then these fields satisfy ∑_i=1ⁿ((n+1)/2−i)p_i=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections.     

Nonergodicity and dynamical approach to the anharmonic oscillator

General lower bounds for the time average C^AA(∞)≡lim_T→∞(1/T)∝^T₀ C^AA(t) dt of the correlation C^AA(t)≡A(t)A(0)−A² of an arbitrary variable A are derived, which depend only on the temperature derivatives of the canonical averages of A and the Hamiltonian of the system. The bounds may be used to give good estimations for C^AA(∞) which is different from zero when A is nonergodic. It is important to take care of these terms when dynamical theories made for interacting systems are applied to isolated systems. We show explicitely that our recently developed dynamical approach to phonon systems with quartic anharmonicity yields excellent results for the corresponding isolated system, the anharmonic single well oscillator, when nonvanishing time averages are taken into account.     

Study of the magnetic properties of single-crystal Ba0.6K0.4BiO3

The magnetic properties of single-crystal Ba_0.6K_0.4BiO₃ were studied. The results show that this isotropic superconductor (cubic structure with T_c ≈ 32 K) exhibits irreversibility and relaxation properties similar to those observed in the layered, high temperature superconductors. For fields above 0.1 T, an irreversibility line B_irr = B_irr (0) (1 − t)ⁿ with n = 3/2 and B_irr (0) = 20 T is observed. The comparison among several superconducting systems with different anisotropies suggests that the irreversibility line is unlikely to be the melting line for the YBa₂Cu₃O_7−δ.     

Incommensurability in an exactly-soluble quantal and classical model for a kicked rotator

The Hamiltonian H = 2πp + V(θ) Σ^∞_−∞ δ(t − n)(0 θ < 2π) is solved exactly, classically and quantally; the so lutions depend strongly on . There is no classical chaos and the phase cylinder p, θ is filled with invariant curves, which are finite loops around the cylinder if is sufficiently irrational and are translates of the infinitely long p axis if is rational. Quantal quasi-energy states correspond exactly to these invariant curves: localized in p and extended in θ if is sufficiently irrational, and extended in p and localized in θ if is rational. For a classical or quantal initial pure-momentum state, the energy at time t = n grows as n² if is rational (resonance) and remains bounded if is sufficiently irrational (non-resonance). If is very nearly rational (marginal resonance), the energy may grow as n^λ where λ is expressed in terms of exponents describing the irrationality of and the continuity class of V(θ). If the value of is uncertain, ensemble-averaging over shows that the energy grows ultimately as n, i.e. diffusively, as though under random impulses.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

The role of polarization of Xe by di- and monovalent cations in Xe NMR studies in zeolite A

We consider the role of polarization in the adsorption of Xe in zeolites of type A by direct comparative analysis of the adsorption isotherms, distributions of occupancies, and ¹²⁹Xe NMR chemical shifts of Xe_n in cages containing Ca_xNa_{12 −2x} ions per alpha cage (x = 0, 1, 2, 3, 5). We find that the qualitative trends in the adsorption isotherms, and in the progressions of Xe_n chemical shifts (for n = 0–8 in cages with x = 0, 1 Ca²⁺ ions and for n = 0–5 in cages with x = 2, 3 Ca²⁺ ions) upon increasing the level of Ca²⁺ ion for Na⁺ ion substitution could only be accounted for by including polarization of the Xe atom by the zeolite framework and its ions. This system, which permits observation of individual Xe_n peaks and of directly comparable adsorption isotherms in several cage types, provides a good model system for the interpretation of the more general case in which only the overall average ¹²⁹Xe NMR chemical shift is observed in open network zeolites, arising from free exchange of Xe among cavities of variable occupancy and variable cation distribution.     

Remarks on stochastic non-linear birth and death models

The first part of this paper is an attempt to formulate and motivate additional work on the important problem of obtaining global bounds applicable to the controlled truncation of the paper relates specifically to the linear birth, quadratic death model. Asymptotic results are given for the first finite difference ΔT_m where T_m is the exactly known mean time to extinction starting from state m (m= 0,1,…). These results are in terms of the environmental carrying capacity n^* taken to be large. For m near zero ΔT_me^n*/(n^*)²; whereas, for m near n^*ΔT_m ≈ (π/2)^1/2/(n^*)^3/2. This indicates the vastly different time scales in those two regions of state space - with considerably slower action near extinction than near n^*.     

Effect of cobalt substitution on cationic distribution in LiNi1 − y CoyO2 electrode materials

A crystal chemistry study of LiNi_{1 − y}Co_yO₂ phases, used as positive electrode in lithium batteries, is presented. These materials crystallize in the rhombohedral system (space group: R m) with a layered structure. Rietveld profile refinement of the X-ray data shows that for low substitution amounts ( ≤ 0.20) extra-nickel ions are always present leading to the Li_{1 − z}Ni_{1 + z − t}CotO₂ (t = y(1 + z)) formula (z * > 0), while for y ≥ 0.30, a pure 2D structure is obtained (z = 0). The stabilization of the 2D character of the structure by cobalt substitution in lithium nickelate leads to the improvement of the electrochemical properties.     

A new upper bound formula for the ground state energies of N-boson systems

The energy E_N of an N-body system of pairwise interacting bosons is shown to satisfy the inequality, E_N < [N(N − 1)/n(n − 1)] E_n, where N > n 2. This inequality generalizes the Bruch-Sawada result, E₃ < 3E₂, and is superior in its predictive ability to Lim et al.'s .     

Ising spin glass on a D = 3 hierarchical lattice: Effects of tailed coupling distributions

Within a real-space renormalization-group framework, we approach the cubic lattice through a D = 3 diamond-like hierarchical lattice. The model is a standard, nearest-neighbor, Ising spin glass with coupling constants {J_ij} distributed according to the family of continuous probability distributions P_q(J_ij) ∝ 1/[1 + (q − 1)J_ij²/2J²]^{1/(q − 1)} (if 1 + (q − 1) J_ij²/2J² > 0, and zero otherwise; q ). Such distributions, which arise naturally in the treatment, within the recently proposed nonextensive thermostatistics, of anomalous diffusion, reproduce the usual, Gaussian case, for q → 1. Moreover, they present a second moment J_ij² proportional to (5 − 3q)⁻¹ for q < 5/3, diverging for q ≥ 5/3, but keeping a finite width at midheight. In the limit q → 3, P_q(J_ij) collapses with the abscissa, and so the width at midheight diverges. We compute the q-dependence of the spin-glass critical temperature T_c. We show numerically that T_c does not scale with J_ij^21/2 (contrary to the usual belief), but rather with the width at midheight of P_q(J_ij). Our results suggest that T_c vanishes as −1/q when q → −∞; furthermore, we verified that T_c diverges exponentially when q approaches 3 from below.     

Defect structure of quenched γ-BICOVOX by combined X-ray and neutron powder diffraction

A detailed investigation of the defect structure of the Co doped BIMEVOX solid electrolyte, Bi₂V_{1 − x}Co_xO_{5.5 − 3x/2} (x = 0.1 and x = 0.2), quenched from high temperature, has been carried out using X-ray and neutron powder diffraction data measured at room temperature. The structure is built up from alternating layers of [Bi₂O₂]_n²ⁿ⁺ and [V_{1 − x}Co_xO_{3.5 − 3x/2}]_n²ⁿ⁻ with disorder limited to the vanadate layer. The ideal V/Co co-ordination is octahedral with corner sharing of equatorial oxygens. The refinements show that the true structure is distorted, with disorder in both apical and equatorial oxygens and oxygen vacancies concentrated in the equatorial positions. Detailed analysis of the oxygen site occupancies reveals two main types of V/Co co-ordination viz. distorted octahedral and distorted tetrahedral. The majority of the sites in both compositions are tetrahedral.     

Dilatometry of the high-temperature proton conductor Ba3Ca1.18Nb1.82O9 − δ

Firstly, the production of solid bulk specimens of the proton conductor Ba₃Ca_1.18Nb_1.82O_{9 − gd} (BCN18) of known water content up to [H^.] = n_H/n_Ba = 0.16 is described. Secondly, measuring the length change of such samples versus water content [H^.] demonstrated that the sample lengths increased linearly with a slope of (Δl/l)/[H^.] = (2.13 ±0.07) × 10⁻². Thirdly, the density of bulk samples was found to decrease linearly with water content [H^.]. This decrease was in good agreement with the above values derived from the length change. Fourthly, high temperature dilatometry showed that samples reach the thermodynamic solubility values in water vapor atmospheres only at temperatures above 700 °C. Two time scales were observed for the time-dependence of the elongation upon exposure to water vapor. A fast process occurred within minutes above 700 °C, a slow one took several hours. The fast one was identified as the chemical diffusion of the diffusion pair H^. and V_o^. which is required for the water uptake and loss of BCN18. The chemical diffusivity of water is described by the parameters D₀ = (0.022 ± 0.002) cm²/s and ΔH* = (0.79 ± 0.05) eV.     

A note on the Wodzicki residue

In this note we explain the relationship of the Wodzicki residue of (certain powers of) an elliptic differential operator P acting on sections of a complex vector bundle E over a closed compact manifold M and the asymptotic expansion of the trace of the corresponding heat operator e^−tP. In the special case of a generalized laplacian Δ and dim M > 2, we thereby obtain a simple proof of the fact already shown in [KW], that the Wodzicki residue res(Δ^−n/2+1) is the integral of the second coefficient of the heat kernel expansion of Δ up to a proportional factor.     

Domain-wall supergravities from sphere reduction

Kaluza-Klein sphere reductions of supergravities that admit Ads × Sphere vacuum solutions are believed to be consistent. The examples include the S⁴ and S⁷ reductions of eleven-dimensional supergravity, and the S⁵ reduction of ten-dimensional type IIB supergravity . In this paper we provide evidence that sphere reductions of supergravities that admit instead Domain-wallxSphere vacuum solutions are also consistent, where the background can be viewed as the near-horizon structure of a dilatonic p-brane of the theory. The resulting lower-dimensional theory is a gauged supergravity that admits a domain wall, rather than AdS, as a vacuum solution. We illustrate this consistency by taking the singular limits of certain modulus parameters, for which the originalSⁿ compactifying spheres (n = 4, 5 or 7) becomes S^p × R^q, with p = n − q < n. The consistency of the S⁴, S⁷ reductions then implies the consistency of the ^Sp reductions of the lower-dimensional supergravities. In particular, we obtain explicit non-linear ansätze for the S³ reduction of type IIA and heterotic supergravities, restricting to the U(1)² subgroup of the SO(4) gauge group of S³. We also study the black-hole solutions in the lower-dimensional gauged supergravities with domain-wall backgrounds. We find new domain-wall black holes which are not the singular-modulus limits of the AdS black holes of the original theories, and we obtain their Killing spinors.     

Magnetic properties of the Bi1.95Sr2.05−xLaxCuOy (Bi-2201) superconducting phase

We have investigated the reversible mixed-state magnetization M of three lanthanum substituted Bi_1.95Sr_2.05−xLa_xCuO_y (Bi-2201) ceramic samples having different critical temperatures T_c ranging from 20.0 to 35.5 K. As for the Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) phase, we found that anisotropy of Bi-2201 is large. A manifestation of this anisotropy is the field independent magnetization M^* observed at a temperature T^*. In the framework of the London model, and including thermal fluctuations of vortices, we found for the temperature dependence of the penetration depth λ_ab(T) = λ_ab(0)[1 − (T/T_c0)ⁿ]^−1/2, with n 1.7 and λ_ab (T = 0) 4000 Å. The estimated upper critical fields μ₀H_c2,c are of the order of 10 T. We observe a peculiar negative slope M/T at low temperature and sufficiently high external magnetic field. This feature seems to be a characteristic of the Bi-2201 phase. However, we do not know whether it is associated with the superconducting mixed-state. A small amount of magnetic impurities could also be responsible for this behavior. Finally, the behavior of the reversible magnetization of the Bi-2201 samples investigated, which are situated at the optimal and in the overdoped region, did not indicate any unusual temperature dependence for the upper critical field H_c2,c.     

Synthesis and characterization of the Aurivillius phases Bi2 − xPbxSr1 − xNdxNb2O9

The n = 2 Aurivillius phase Bi_{2 − x}Pb_xSr_{1 − x}Nd₂O₉ was successfully synthesized as a ceramic material over the whole range of simultaneous, charge compensated substitution x = 0–1.0. Structural investigations were performed by Rietveld refinement applying different space groups Fmmm and A2₁am, and additionally by X-ray absorption spectroscopy (EXAFS) on the Nd L_III-edge, confirming the accommodation of Nd on the atomic sites of Sr, which implies the substitution of Bi³⁺ by the isoelectronic Pb²⁺. The ferroelectric transition temperature T_c = 270 °C of the substituted powders with x = 0.4 and 1.0 is distinctly reduced compared to the unsubstituted sample with T_c = 450 °C. In temperature resolved powder X-ray diffraction patterns no structural phase transition could be detected.     

Effects of cation- or oxide ion-defect on conductivities of apatite-type La–Ge–O system ceramics

A series of apatite-type La–Ge–O ceramics were prepared and their cation-defect at the 4f+6h sites and oxide ion-defect at 2a site were investigated. In La_xGe₆O_12+1.5x ceramics of x=6–12, the higher conductivities were obtained in the region of apatite composition, La_x(GeO₄)₆O_1.5x−12 (x=8–9.33), and the highest conductivity was achieved for La₉(GeO₄)₆O_1.5 (x=9), where the number of cation (La³⁺) occupying the 4f+6h sites is 9 and the number of oxide ion occupying the 2a site is 1.5. The ceramics with cation- and oxide ion-defects were La_9−0.66xSr_x(GeO₄)₆O_1.5 (x=0–1), La_9−1.33xZr_x(GeO₄)₆O_1.5 (x=0–1), La_9−xSr_x(GeO₄)₆O_1.5−0.5x (x=0–3), La_9−xZr_x(GeO₄)₆O_1.5+0.5x (x=0–1), La_x(GeO₄)_3x−21(AsO₄)_27−3xO_1.5 (x=0–3), La_x(GeO₄)_33−3x(AlO₄)_3x−27O_1.5 (x=0–3), La₉(GeO₄)_6−x (AlO₄)_xO_1.5−0.5x (x=0–3), La₉(GeO₄)_6−x(AsO₄)_xO_1.5+0.5x (x=0–1), La_9.33−xSr_x(GeO₄)₆O_2−0.5x (x=0–1.2) and La_x(GeO₄)_4.5(AlO₄)_1.5O_1.5x−12.75 (x=8.8–9.83), which were prepared by the partial substitution of La³⁺and GeO₄⁴⁻of the basic apatite La₉(GeO₄)₆O_1.5 with Sr²⁺ or Zr⁴⁺ and AlO₄⁵⁻ or AsO₄³⁻. Such substitutions lowered the conductivity of La₉(GeO₄)₆O_1.5. These results were discussed by the electrostatic interaction between Sr²⁺, Zr⁴⁺, AlO₄⁵⁻ or AsO₄³⁻ and oxide ion as a conductive species.