Shannon entropies and Fisher information of K-shell electrons of neutral atoms

We represent the two K-shell electrons of neutral atoms by Hylleraas-type wave function which fulfils the exact behavior at the electron–electron and electron-nucleus coalescence points and, derive a simple method to construct expressions for single-particle position- and momentum-space charge densities, $\rho (\mathit{r})$ and $\gamma (\mathit{p})$ respectively. We make use of the results for $\rho (\mathit{r})$ and $\gamma (\mathit{p})$ to critically examine the effect of correlation on bare (uncorrelated) values of Shannon information entropies (S) and of Fisher information (F) for the K-shell electrons of atoms from helium to neon. Due to inter-electronic repulsion the values of the uncorrelated Shannon position-space entropies are augmented while those of the momentum-space entropies are reduced. The corresponding Fisher information are found to exhibit opposite behavior in respect of this. Attempts are made to provide some plausible explanation for the observed response of S and F to electronic correlation.     

Supersymmetric extensions of Schrödinger-invariance

The set of dynamic symmetries of the scalar free Schrödinger equation in d space dimensions gives a realization of the Schrödinger algebra that may be extended into a representation of the conformal algebra in $d+2$ dimensions, which yields the set of dynamic symmetries of the same equation where the mass is not viewed as a constant, but as an additional coordinate. An analogous construction also holds for the spin-$\frac{1}{2}$ Lévy-Leblond equation. An $N=2$ supersymmetric extension of these equations leads, respectively, to a ‘super-Schrödinger’ model and to the $(3|2)$-supersymmetric model. Their dynamic supersymmetries form the Lie superalgebras $\mathfrak{osp}(2|2)⋉\mathfrak{sh}(2|2)$ and $\mathfrak{osp}(2|4)$, respectively. The Schrödinger algebra and its supersymmetric counterparts are found to be the largest finite-dimensional Lie subalgebras of a family of infinite-dimensional Lie superalgebras that are systematically constructed in a Poisson algebra setting, including the Schrödinger–Neveu–Schwarz algebra ${\mathfrak{sns}}^{(N)}$ with N supercharges. Covariant two-point functions of quasiprimary superfields are calculated for several subalgebras of $\mathfrak{osp}(2|4)$. If one includes both $N=2$ supercharges and time-inversions, then the sum of the scaling dimensions is restricted to a finite set of possible values.     

The effect of Ag adsorption on the structural,electronic, and optical properties of the ZnO(101̅0) surface: A first-principles study

The effect of the Ag adsorption on the structural, electronic and optical properties of the clean ZnO$(10\bar{1}0)$ surface was investigated using the first principles method. The obtained results show that adsorbed Ag atoms transfer charge to the surface which results in a charge accumulation in near-surface region accompanied with a decrease of the work function. On the other hand, our results show that the adsorption of Ag atoms leads also to the new optical absorption peaks in the visible region which could improve ZnO photocatalytical properties.     

Structure and magnetic properties of In2RuMnO6 and In2RuFeO6 : Heavily transition-metal doped In2O3 -type bixbyites

The title compounds have been synthesized by a citrate technique. The crystal structure of these materials has been studied at room temperature from high-resolution neutron powder diffraction data. In, Ru, and M=Mn,Fe are distributed at random over the metal sites of a C-M₂O₃ bixbyite-type structure, space group $Ia\stackrel{?}{3}$, with $a=9.89000\left(3\right)\AA$ for M=Mn and $a=10.07536\left(4\right)\AA$ for M=Fe. It is well known that In₂O₃ is able to dissolve certain amounts of transition metals but, at ambient pressure, the solubility is rather small, lower than $s=0.5$ in In_2?sM_sO₃. Here, we describe a substantial incorporation of magnetic transition metals into In₂O₃ of half of the metal positions ($s=1$), by simple thermal treatment at temperatures in the 1300–1400 °C range. Although a bond-valence study shows unrealistically low valences for Ru ions, which statistically occupy the metal positions, replacing In, the magnetic properties suggest a valence equilibrium Ru³⁺/M³⁺?Ru⁴⁺/M²⁺. In₂RuFeO₆ shows antiferromagnetic interactions below $T_N\approx 95K$, with a very weak ferromagnetism effect at low temperatures.     

Enhanced energy storage and pyroelectric properties of highly (100)-oriented (Pb1−x−yLaxCay)Ti1−x/4O3 thin films derived at low temperature

Highly (100)-oriented (Pb_1?x?yLa_xCa_y)Ti_1?x/4O₃ ($x=0.15$, $y=0.05$; $x=0.1$, $y=0.1$; $x=0.05$, $y=0.15$) thin films were deposited on Pt/Ti/SiO₂/Si substrates at a low temperature of 450?°C via a sol–gel route. It was found that all the (Pb_1?x?yLa_xCa_y)Ti_1?x/4O₃ thin films could be completely crystallized and the content of La/Ca showed a significant effect on the electrical properties of films. Among the three films, the (Pb_1?x?yLa_xCa_y)Ti_1?x/4O₃ ($x=0.1$, $y=0.1$) thin film exhibited the enhanced overall electrical properties, such as a low dielectric loss ($\tan ?\delta <0.08$) and leakage current ($J～4.6\times {10}^{?5}$ A/cm²), a high recoverable energy density (W_re ～ 15 J/cm³), as well as a large pyroelectric coefficient (p ～ 190 μC/m²K) and figure of merit ($F_{\mathrm{d}}^{\prime }～77\mathrm{\mu }\text{C}/{\text{m}}^2$K). The findings suggest that the fabricated thin films with a good (100) orientation can be an attractive candidate for applications in Si-based energy storage and pyroelectric devices.     

Angular energy flow in perturbative QCD

We discuss a general way in which QCD can be checked in lepton-induced reactions — even with low statistics data. This is the “angular energy flow”, or the average energy fraction outside a cone of opening angle 2σ about the principal jet axis. in the final state of deep inelastic reactions. We illustrate this method by a perturbative calculation of the angular energy flow in $e^{+}{e}^{?}\to q\overline{q}g\to$ jets. This perturbative approach can be extended to other deep inelastic reactions wit h gluon jets. At high enough energy, it should test QCD beyond lowest order in α_s.     

Sub- and super-diffusion on Cantor sets: Beyond the paradox

There is no way to build a nontrivial Markov process having continuous trajectories on a totally disconnected fractal embedded in the Euclidean space. Accordingly, in order to delineate the diffusion process on the totally disconnected fractal, one needs to relax the continuum requirement. Consequently, a diffusion process depends on how the continuum requirement is handled. This explains the emergence of different types of anomalous diffusion on the same totally disconnected set. In this regard, we argue that the number of effective spatial degrees of freedom of a random walker on the totally disconnected Cantor set is equal to $n_{sp}=[D]+1$, where $[D]$ is the integer part of the Hausdorff dimension of the Cantor set. Conversely, the number of effective dynamical degrees of freedom $(d_s)$ depends on the definition of a Markov process on the totally disconnected Cantor set embedded in the Euclidean space $E^n$$(n\ge n_{sp})$. This allows us to deduce the equation of diffusion by employing the local differential operators on the $F^{\alpha }$-support. The exact solutions of this equation are obtained on the middle-? Cantor sets for different kinds of the Markovian random processes. The relation of our findings to physical phenomena observed in complex systems is highlighted.