Klein–Gordon equation for a charged particle in space-varying electromagnetic fields–A systematic study via the Laplace transform

Exact solutions of the Klein–Gordon equation for a charged particle in the presence of three spatially varying electromagnetic fields, namely, (i) $\overrightarrow{E}=\alpha {\beta }_0{e}^{?\alpha x_2}{\widehat{x}}_2,$$\overrightarrow{B}=\alpha {\beta }_1{e}^{?\alpha x_2}{\widehat{x}}_3$ (ii) $\overrightarrow{E}=\frac{{\beta }_0^{{}^{\prime }}}{x_2^2}{\widehat{x}}_2,$$\overrightarrow{B}=\frac{{\beta }_1^{{}^{\prime }}}{x_2^2}{\widehat{x}}_3,$ and (iii) $\overrightarrow{E}=\frac{2{\beta }_0^{{}^{\prime }}}{x_2^3}{\widehat{x}}_2,$$\overrightarrow{B}=\frac{2{\beta }_1^{{}^{\prime }}}{x_2^3}{\widehat{x}}_3,$ are studied. All these fields are generated from a systematic study of a particular type of differential equation whose coefficients are linear in the independent variable. The Laplace transform approach is used to find the solutions, and the corresponding eigenfunctions are expressed in terms of the hypergeometric functions ?₁F₁(a′, b′; x) for the first two cases of the above configurations, while the same are expressed in terms of the Bessel functions of first kind, J_n(x), for the last case.     

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.     

On the geometry of null hypersurfaces in Minkowski space

The present work is divided into three parts. First we study the null hypersurfaces of the Minkowski space ${\mathbb{R}}_1^{n+2}$, classifying all rotation null hypersurfaces in ${\mathbb{R}}_1^{n+2}$. In the second part we start our analysis of the submanifold geometry of the null hypersurfaces. In the particular case of the $(n+1)$-dimensional light cone, we characterize its totally umbilical spacelike hypersurfaces, show the existence of non-totally umbilical ones and give a uniqueness result for the minimal spacelike rotation surfaces in the $3$-dimensional light cone. In the third and final part we consider an isolated umbilical point on a spacelike surface immersed in the 3-dimensional light cone of ${\mathbb{R}}_1^4$ and obtain the differential equation of the principal configuration associated to this point, showing that every classical generic Darbouxian principal configuration appears in this context.     

Toward a topological scenario for high-temperature superconductivity of copper oxides

The structure of the joint phase diagram demonstrating high-$T_c$ superconductivity of copper oxides is studied on the basis of the theory of interaction-induced flat bands. Prerequisites for an associated topological rearrangement of the Landau state are established, and related non-Fermi-liquid (NFL) behavior of the normal states of cuprates is investigated. We focus on manifestations of this behavior in the electrical resistivity $\rho (T)$, especially the observed gradual crossover from normal-state T-linear behavior $\rho (T,x)=A_1(x)T$ at doping x below the critical value $x_c^h$ of hole doping for termination of superconductivity, to T-quadratic behavior at $x>x_c^h$, which is incompatible with predictions of the conventional quantum-critical-point scenario. It is demonstrated that the slope of the coefficient $A_1$ is universal, being the same on both boundaries of the joint phase diagram of cuprates, in agreement with available experimental data.     

Quantum point contact conductance in normal metal/insulator/ metal/dx2−y2+idxy mixed wave superconductor junctions

The tunneling conductance in a normal metal/insulator/metal/$d_{x^2?y^2}+i{d}_{xy}$ mixed wave superconductor (N/I/N/$d_{x^2?y^2}+i{d}_{xy}$) junction is calculated, where the N/I/N region is a quantum wire. It is found in the single-mode case that the magnitude of the tunneling conductance near zero voltage is enhanced due to the Andreev bound state by quasiparticles with perpendicular and horizontal injection, and the zero-bias conductance varies with $L$ ($L$ is the distance from insulating layer to the interface of N/$d_{x^2?y^2}+i{d}_{xy}$ mixed wave superconductor). Splitting of the zero-bias conductance peak appears in the quantum point contact tunneling spectra for an N/I/N/$d_{x^2?y^2}+i{d}_{xy}$ junction, and several subgap peaks can split at the same time. On increasing both $L$ and the magnitude ratio of the two components for the $d_{x^2?y^2}+i{d}_{xy}$ mixed wave, the subgap resonances exhibit an alternately high and low behavior inside the energy gap. These results are different from those in d-wave and p-wave superconductor junctions.     

An orthorhombic chromium-center in the spinel MgAl2O4

In Cr-doped MgAl₂O₄ most of the Cr³⁺-ions occupy normal B-sites. In addition to this axial center we report here the presence of an orthorhombic Cr³⁺-center. The ESR-spectra of this new center can be described by the spin Hamiltonian:

$?=\mathit{D}\left[S_z^2?\frac{1}{3}\mathit{S}\left(S+1\right)\right]+g_x\beta H_x{S}_x+g_y\beta H_y{S}_y+g_z\beta H_z{S}_z+\mathit{E}\left(S_x^2?S_y^2\right)$

, with S=3/2. The principal axes of the center are along [111]=Z, $\left[111\right]=Z,\left[1\overline{1}0\right]=Y$ and $\left[\overline{1}\overline{1}2\right]=X$. The values of the parameters are: g_z=1·950±0·005, g_x=g_y=1·915±0·015, D=+0·903cm^?1±0·003 cm^?1 and E=+0·084 cm^?1±0·005 cm^?1. The intensity of the lines is about ten times lower than that of the axial Cr³⁺-center.     

Monopoles on the Bryant–Salamon G2-manifolds

$G_2$-monopoles are solutions to gauge theoretical equations on noncompact $7$-manifolds of $G_2$ holonomy. We shall study this equation on the $3$ Bryant–Salamon manifolds. We construct examples of $G_2$-monopoles on two of these manifolds, namely the total space of the bundle of anti-self-dual two forms over the ${\mathbb{S}}^4$ and ${\mathbb{C}\mathbb{P}}^2$. These are the first nontrivial examples of $G_2$-monopoles.Associated with each monopole there is a parameter $m\in {\mathbb{R}}^{+}$, known as the mass of the monopole. We prove that under a symmetry assumption, for each given $m\in {\mathbb{R}}^{+}$ there is a unique monopole with mass $m$. We also find explicit irreducible $G_2$-instantons on ${\Lambda }_{-}^2\left({\mathbb{S}}^4\right)$ and on ${\Lambda }_{-}^2\left({\mathbb{C}\mathbb{P}}^2\right)$.The third Bryant–Salamon $G_2$-metric lives on the spinor bundle over the $3$-sphere. In this case we produce a vanishing theorem for monopoles.