Levinson's theorem for the Schr\"{o}dinger equation in two dimensions

Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically symmetric potential in two dimensions is re-established by the Sturm-Liouville theorem. The critical case, where the Schr\"{o}dinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison with Levinson's theorem in non-critical case, the half bound state for $P$ wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of $P$ wave at zero energy to increase an additional $\pi$.Comment: Latex 11 pages, no figure and accepted by P.R.A (in August); Email: [email protected], [email protected]

Tuning Jeff = 1/2 Insulating State via Electron Doping and Pressure in Double-Layered Iridate Sr3Ir2O7

Sr3Ir2O7 exhibits a novel Jeff=1/2 insulating state that features a splitting between Jeff=1/2 and 3/2 bands due to spin-orbit interaction. We report a metal-insulator transition in Sr3Ir2O7 via either dilute electron doping (La3+ for Sr2+) or application of high pressure up to 35 GPa. Our study of single-crystal Sr3Ir2O7 and (Sr1-xLax)3Ir2O7 reveals that application of high hydrostatic pressure P leads to a drastic reduction in the electrical resistivity by as much as six orders of magnitude at a critical pressure, PC = 13.2 GPa, manifesting a closing of the gap; but further increasing P up to 35 GPa produces no fully metallic state at low temperatures, possibly as a consequence of localization due to a narrow distribution of bonding angles {\theta}. In contrast, slight doping of La3+ ions for Sr2+ ions in Sr3Ir2O7 readily induces a robust metallic state in the resistivity at low temperatures; the magnetic ordering temperature is significantly suppressed but remains finite for (Sr0.95La0.05)3Ir2O7 where the metallic state occurs. The results are discussed along with comparisons drawn with Sr2IrO4, a prototype of the Jeff = 1/2 insulator.Comment: five figure

The Relativistic Levinson Theorem in Two Dimensions

In the light of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation in two dimensions is established as a relation between the total number $n_{j}$ of the bound states and the sum of the phase shifts $\eta_{j}(\pm M)$ of the scattering states with the angular momentum $j$: $$\eta_{j}(M)+\eta_{j}(-M)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$$ $$~~~=\left\{\begin{array}{ll} (n_{j}+1)\pi &{\rm when~a~half~bound~state~occurs~at}~E=M ~~{\rm and}~~ j=3/2~{\rm or}~-1/2\\ (n_{j}+1)\pi &{\rm when~a~half~bound~state~occurs~at}~E=-M~~{\rm and}~~ j=1/2~{\rm or}~-3/2\\ n_{j}\pi~&{\rm the~rest~cases} . \end{array} \right.$$ \noindent The critical case, where the Dirac equation has a finite zero-momentum solution, is analyzed in detail. A zero-momentum solution is called a half bound state if its wave function is finite but does not decay fast enough at infinity to be square integrable.Comment: Latex 14 pages, no figure, submitted to Phys.Rev.A; Email: [email protected], [email protected]

Thermodynamic Properties of Supported and Embedded Metallic Nanocrystals: Gold on/in SiO2

We report on the calculations of the cohesive energy, melting temperature and vacancy formation energy for Au nanocrystals with different size supported on and embedded in SiO2. The calculations are performed crossing our previous data on the surface free energy of the supported and embedded nanocrystals with the theoretical surface-area-difference model developed by W. H. Qi for the description of the size-dependent thermodynamics properties of low-dimensional solid-state systems. Such calculations are employed as a function of the nanocrystals size and surface energy. For nanocrystals supported on SiO2, as results of the calculations, we obtain, for a fixed nanocrystal size, an almost constant cohesive energy, melting temperature and vacancy formation energy as a function of their surface energy; instead, for those embedded in SiO2, they decreases when the nanocrystal surface free energy increases. Furthermore, the cohesive energy, melting temperature and vacancy formation energy increase when the nanocrystal size increases: for the nanocrystals on SiO2, they tend to the values of the bulk Au; for the nanocrystals in SiO2 in correspondence to sufficiently small values of their surface energy, they are greater than the bulk values. In the case of the melting temperature, this phenomenon corresponds to the experimentally well-known superheating process

Bridgeness: A Local Index on Edge Significance in Maintaining Global Connectivity

Edges in a network can be divided into two kinds according to their different roles: some enhance the locality like the ones inside a cluster while others contribute to the global connectivity like the ones connecting two clusters. A recent study by Onnela et al uncovered the weak ties effects in mobile communication. In this article, we provide complementary results on document networks, that is, the edges connecting less similar nodes in content are more significant in maintaining the global connectivity. We propose an index named bridgeness to quantify the edge significance in maintaining connectivity, which only depends on local information of network topology. We compare the bridgeness with content similarity and some other structural indices according to an edge percolation process. Experimental results on document networks show that the bridgeness outperforms content similarity in characterizing the edge significance. Furthermore, extensive numerical results on disparate networks indicate that the bridgeness is also better than some well-known indices on edge significance, including the Jaccard coefficient, degree product and betweenness centrality.Comment: 10 pages, 4 figures, 1 tabl

Get my pizza right: Repairing missing is-a relations in ALC ontologies (extended version)

With the increased use of ontologies in semantically-enabled applications, the issue of debugging defects in ontologies has become increasingly important. These defects can lead to wrong or incomplete results for the applications. Debugging consists of the phases of detection and repairing. In this paper we focus on the repairing phase of a particular kind of defects, i.e. the missing relations in the is-a hierarchy. Previous work has dealt with the case of taxonomies. In this work we extend the scope to deal with ALC ontologies that can be represented using acyclic terminologies. We present algorithms and discuss a system

Anisotropic softening of magnetic excitations in lightly electron doped Sr2_2IrO4_4

The magnetic excitations in electron doped (Sr$_{1-x}$La$_x$)$_2$IrO$_4$ with $x = 0.03$ were measured using resonant inelastic X-ray scattering at the Ir $L_3$-edge. Although much broadened, well defined dispersive magnetic excitations were observed. Comparing with the magnetic dispersion from the parent compound, the evolution of the magnetic excitations upon doping is highly anisotropic. Along the anti-nodal direction, the dispersion is almost intact. On the other hand, the magnetic excitations along the nodal direction show significant softening. These results establish the presence of strong magnetic correlations in electron doped Sr$_{1-x}$La$_x$)$_2$IrO$_4$ with close analogies to the hole doped cuprates, further motivating the search for high temperature superconductivity in this system