Measuring the Hausdorff Dimension of Quantum Mechanical Paths

We measure the propagator length in imaginary time quantum mechanics by Monte Carlo simulation on a lattice and extract the Hausdorff dimension $d_{H}$. We find that all local potentials fall into the same universality class giving $d_{H}=2$ like the free motion. A velocity dependent action ($S \propto \int dt \mid \vec{v} \mid^{\alpha}$) in the path integral (e.g. electrons moving in solids, or Brueckner's theory of nuclear matter) yields $d_{H}=\frac{\alpha }{\alpha - 1}$ if $\alpha > 2$ and $d_{H}=2$ if $\alpha \leq 2$. We discuss the relevance of fractal pathes in solid state physics and in $QFT$, in particular for the Wilson loop in $QCD$.Comment: uuencoded and compressed shell archive file. 8 pages with 7 figure

Evolution of unoccupied resonance during the synthesis of a silver dimer on Ag(111)

Silver dimers were fabricated on Ag(111) by single-atom manipulation using the tip of a cryogenic scanning tunnelling microscope. An unoccupied electronic resonance was observed to shift toward the Fermi level with decreasing atom-atom distance as monitored by spatially resolved scanning tunnelling spectroscopy. Density functional calculations were used to analyse the experimental observations and revealed that the coupling between the adsorbed atoms is predominantly direct rather than indirect via the Ag(111) substrate.Comment: 9 pages, 3 figure

Defect distribution in a-plane GaN on Al2O3

The authors studied the structural and point defect distributions of hydride vapor phase epitaxial GaN film grown in the [11−20] a direction on (1−102) r-plane sapphire with metal-organic vapor phase deposited a-GaN template using transmission electron microscopy, secondary ion mass spectrometry, and positron annihilation spectroscopy. Grown-in extended and point defects show constant behavior as a function of thickness, contrary to the strong nonuniform defect distribution observed in GaN grown along the [0001] direction. The observed differences are explained by orientation-dependent and kinetics related defect incorporation.Peer reviewe

Interfacial separation between elastic solids with randomly rough surfaces: comparison of experiment with theory

We study the average separation between an elastic solid and a hard solid with a nominal flat but randomly rough surface, as a function of the squeezing pressure. We present experimental results for a silicon rubber (PDMS) block with a flat surface squeezed against an asphalt road surface. The theory shows that an effective repulse pressure act between the surfaces of the form p proportional to exp(-u/u0), where u is the average separation between the surfaces and u0 a constant of order the root-mean-square roughness, in good agreement with the experimental results.Comment: 6 pages, 10 figure

Tuning the properties of complex transparent conducting oxides: role of crystal symmetry, chemical composition and carrier generation

The electronic properties of single- and multi-cation transparent conducting oxides (TCOs) are investigated using first-principles density functional approach. A detailed comparison of the electronic band structure of stoichiometric and oxygen deficient In$_2$O$_3$, $\alpha$- and $\beta$-Ga$_2$O$_3$, rock salt and wurtzite ZnO, and layered InGaZnO$_4$ reveals the role of the following factors which govern the transport and optical properties of these TCO materials: (i) the crystal symmetry of the oxides, including both the oxygen coordination and the long-range structural anisotropy; (ii) the electronic configuration of the cation(s), specifically, the type of orbital(s) -- $s$, $p$ or $d$ -- which form the conduction band; and (iii) the strength of the hybridization between the cation's states and the p-states of the neighboring oxygen atoms. The results not only explain the experimentally observed trends in the electrical conductivity in the single-cation TCO, but also demonstrate that multicomponent oxides may offer a way to overcome the electron localization bottleneck which limits the charge transport in wide-bandgap main-group metal oxides. Further, the advantages of aliovalent substitutional doping -- an alternative route to generate carriers in a TCO host -- are outlined based on the electronic band structure calculations of Sn, Ga, Ti and Zr-doped InGaZnO$_4$. We show that the transition metal dopants offer a possibility to improve conductivity without compromising the optical transmittance

Assortativity Decreases the Robustness of Interdependent Networks

It was recently recognized that interdependencies among different networks can play a crucial role in triggering cascading failures and hence system-wide disasters. A recent model shows how pairs of interdependent networks can exhibit an abrupt percolation transition as failures accumulate. We report on the effects of topology on failure propagation for a model system consisting of two interdependent networks. We find that the internal node correlations in each of the two interdependent networks significantly changes the critical density of failures that triggers the total disruption of the two-network system. Specifically, we find that the assortativity (i.e. the likelihood of nodes with similar degree to be connected) within a single network decreases the robustness of the entire system. The results of this study on the influence of assortativity may provide insights into ways of improving the robustness of network architecture, and thus enhances the level of protection of critical infrastructures