p(x) and Tc(x) characteristics in the Y 1−b(Ca)bBa2Cu3O6+x cuprate family

A model has been proposed to calculate the $p\left(x\right)$ and $T_c\left(x\right)$ dependences in the Y _1?b(Ca)_bBa₂Cu₃O_6+x high-$T_c$ cuprate family and applied to $b=0$, $b=0.1$, and $b=0.2$ cases, for which experimental data exist in the literature. The results obtained imply that the Ca efficiency to provide holes is independent of the basal plane oxygen concentration, which is consistent with a view that electrons from CuO₂ layers would go primarily to Ca since it is twice closer than oxygen (in addition, the chain oxygen is screened by a layer made up of Ba and O(4) ions). It is shown that, in fully oxygenized compounds ($x=1$) the average efficiency, $\chi$, of a chain oxygen to attract an electron from the two nearby layers is reduced by the Ca insertion, though not because the charge transfer mechanism is in itself weakened by Ca, but because a part of electrons that are otherwise available in CuO${}_2$ layers has already been removed by the substitution of Y ³⁺ with Ca²⁺. It has been found that the $b$-dependence of the average oxygen doping efficiency can be fairly accurately described by the following relation: $\chi \left(b\right)=0.39\times (1?0.78b)$. The calculated $p\left(x\right)$ and $T_c\left(x\right)$ dependences are in very good agreement with the available experimental data.     

Pressure dependence of negative thermal expansion in Zr2(WO4)(PO4)2

Negative thermal expansion materials can experience significant stresses when they are used in composites. Under ambient conditions Zr₂(WO₄)(PO₄)₂ displays anisotropic negative thermal expansion (NTE) (${\alpha }_v=?14.0\left(10\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_a=?7.9\left(5\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_b=2.5\left(5\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_c=?8.7\left(2\right)\times 10^{?6}{K}^{?1}$ at 0 GPa). The effect of hydrostatic pressure on its thermal expansion characteristics was investigated by neutron diffraction between 300 and 60 K at pressures up to 0.3 GPa. No phase transitions were observed in the pressure and temperature range examined. The material was found to have a bulk modulus, B₀, of 61.3(8) GPa at ambient temperature, and unlike some other NTE materials, pressure had no detectable effect on thermal expansion (${\alpha }_v=?14.2\left(8\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_a=?7.9\left(3\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_b=2.9\left(5\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_c=?9.2\left(2\right)\times 10^{?6}{K}^{?1}$ at 0.3 GPa).     

ESR in a gapped Anderson model

We applied the numerical renormalization group method to study the electron spin resonance (ESR) of a single-impurity Anderson model with a gap $\Delta$ in the conduction electron density of states, centered at the Fermi level. We analyzed the relaxation rate $1/T_1$ of a magnetic probe located at a position $\overrightarrow{R}$ around the Anderson impurity. It presents different behaviors for the symmetric and the asymmetric case. For the symmetric case and any $\Delta >0$, $1/T_1$ goes to a constant for $T?{\Gamma }_{\text{k}}$ (Kondo resonance). $1/T_1$ decreases monotonically to zero only for $\Delta =0$. For the asymmetric case, there is a $\Delta$ under which $1/T_1$ decreases monotonically to zero as $T\to 0$, and above which $1/T_1$ saturates, as occurs in the symmetric case for $\Delta >0$. This behavior indicates a quantum phase transition from the quenched to the unquenched magnetic moment in the ground state of the Anderson ion.     

Effect upon universal order of Hubble expansion

The level of order $R$ in a spherical system of radius $r_0$ with a probability amplitude function $\psi \left(x\right),x=r,\theta ,?$ obeys $R=(1/2)r_0^{2}I$, where $I=4\int dx{\left|?\psi \right|}^2$ is its Fisher information level. We show that a flat space universe obeying the Robertson–Walker metric has an invariant value of the order as it undergoes either uniform Hubble expansion or contraction. This means that Hubble expansion per se does not cause a loss of universal order as time progresses. Instead, coarse graining processes characterizing decoherence and friction might cause a loss of order. Alternatively, looking backward in time, i.e. under Hubble contraction, as the big bang is approached and the Hubble radius $r_0$ approaches small values, the structure in the amplitude function $\psi \left(x\right)$ becomes ever more densely packed, increasing all local slopes $?\psi$ and causing the Fisher information $I$ to approach unboundedly large values. As a speculation, this ever-well locates the initial position of the universe in a larger, multiverse.