Anisotropic Radial Layout for Visualizing Centrality and Structure in Graphs

This paper presents a novel method for layout of undirected graphs, where nodes (vertices) are constrained to lie on a set of nested, simple, closed curves. Such a layout is useful to simultaneously display the structural centrality and vertex distance information for graphs in many domains, including social networks. Closed curves are a more general constraint than the previously proposed circles, and afford our method more flexibility to preserve vertex relationships compared to existing radial layout methods. The proposed approach modifies the multidimensional scaling (MDS) stress to include the estimation of a vertex depth or centrality field as well as a term that penalizes discord between structural centrality of vertices and their alignment with this carefully estimated field. We also propose a visualization strategy for the proposed layout and demonstrate its effectiveness using three social network datasets.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Conductance Increase by Electron-Phonon Interaction in Quantum Wires

We investigate the influence of electron-phonon interactions on the DC-conductance $\Gamma$ of a quantum wire in the limit of one occupied subband. At zero temperature, a Tomonaga-Luttinger-like renormalization of $\Gamma$ to a value slightly larger than $2e^{2}/h$ is calculated for a realistic quantum wire model.Comment: 12 pages RevTeX, no figure. Appears in Phys. Rev.

Finite-size scaling from self-consistent theory of localization

Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the finite-size scaling procedure used for studies of the critical behavior in d-dimensional case and based on the use of auxiliary quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good agreement with numerical results: it signifies the absence of essential contradictions with the Vollhardt and Woelfle theory on the level of raw data. The results \nu=1.3-1.6, usually obtained at d=3 for the critical exponent of the correlation length, are explained by the fact that dependence L+L_0 with L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\nu} with \nu>1. For dimensions d\ge 4, the modified scaling relations are derived; it demonstrates incorrectness of the conventional treatment of data for d=4 and d=5, but establishes the constructive procedure for such a treatment. Consequences for other variants of finite-size scaling are discussed.Comment: Latex, 23 pages, figures included; additional Fig.8 is added with high precision data by Kramer et a

GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs

We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer), provides a unified framework for scalable computation and presentation of high-quality suboptimal solutions and bounds for a number of widely studied combinatorial optimisation problems. Efficient representation and applicability to large-scale graphs and complex networks are particularly considered in its design. The problems currently supported include maximum clique, graph colouring, maximum independent set, minimum vertex clique covering, minimum dominating set, as well as the longest simple cycle problem. Suboptimal solutions and intervals for optimal objective values are estimated using scalable heuristics. The tool is designed with extensibility in mind, with the view of further problems and both new fast and high-performance heuristics to be added in the future. GraphCombEx has already been successfully used as a support tool in a number of recent research studies using combinatorial optimisation to analyse complex networks, indicating its promise as a research software tool

Potential super-hard Osmium di-nitride with fluorite structure: First-principles calculations

We have performed systematic first-principles calculations on di-carbide, -nitride, -oxide and -boride of platinum and osmium with the fluorite structure. It is found that only PtN$_{2}$, OsN$_{2}$ and OsO$_{2}$ are mechanically stable. In particular OsN$_{2}$ has the highest bulk modulus of 360.7 GPa. Both the band structure and density of states show that the new phase of OsN$_{2}$ is metallic. The high bulk modulus is owing to the strong covalent bonding between Os 5\textit{d} and N 2\textit{p} states and the dense packed fluorite structure.Comment: Phys. Rev. B 74,125118 (2006

Coherent Electron-Phonon Coupling in Tailored Quantum Systems

The coupling between a two-level system and its environment leads to decoherence. Within the context of coherent manipulation of electronic or quasiparticle states in nanostructures, it is crucial to understand the sources of decoherence. Here, we study the effect of electron-phonon coupling in a graphene and an InAs nanowire double quantum dot. Our measurements reveal oscillations of the double quantum dot current periodic in energy detuning between the two levels. These periodic peaks are more pronounced in the nanowire than in graphene, and disappear when the temperature is increased. We attribute the oscillations to an interference effect between two alternative inelastic decay paths involving acoustic phonons present in these materials. This interpretation predicts the oscillations to wash out when temperature is increased, as observed experimentally.Comment: 11 pages, 4 figure

Scaling near the upper critical dimensionality in the localization theory

The phenomenon of upper critical dimensionality d_c2 has been studied from the viewpoint of the scaling concepts. The Thouless number g(L) is not the only essential variable in scale transformations, because there is the second parameter connected with the off-diagonal disorder. The investigation of the resulting two-parameter scaling has revealed two scenarios, and the switching from one to another scenario determines the upper critical dimensionality. The first scenario corresponds to the conventional one-parameter scaling and is characterized by the parameter g(L) invariant under scale transformations when the system is at the critical point. In the second scenario, the Thouless number g(L) grows at the critical point as L^{d-d_c2}. This leads to violation of the Wegner relation s=\nu(d-2) between the critical exponents for conductivity (s) and for localization radius (\nu), which takes the form s=\nu(d_c2-2). The resulting formulas for g(L) are in agreement with the symmetry theory suggested previously [JETP 81, 925 (1995)]. A more rigorous version of Mott's argument concerning localization due topological disorder has been proposed.Comment: PDF, 7 pages, 6 figure

Wave-packet dynamics at the mobility edge in two- and three-dimensional systems

We study the time evolution of wave packets at the mobility edge of disordered non-interacting electrons in two and three spatial dimensions. The results of numerical calculations are found to agree with the predictions of scaling theory. In particular, we find that the $k$-th moment of the probability density $(t)$ scales like $t^{k/d}$ in $d$ dimensions. The return probability $P(r=0,t)$ scales like $t^{-D_2/d}$, with the generalized dimension of the participation ratio $D_2$. For long times and short distances the probability density of the wave packet shows power law scaling $P(r,t)\propto t^{-D_2/d}r^{D_2-d}$. The numerical calculations were performed on network models defined by a unitary time evolution operator providing an efficient model for the study of the wave packet dynamics.Comment: 4 pages, RevTeX, 4 figures included, published versio

Reverse quantum state engineering using electronic feedback loops

We propose an all-electronic technique to manipulate and control interacting quantum systems by unitary single-jump feedback conditioned on the outcome of a capacitively coupled electrometer and in particular a single-electron transistor. We provide a general scheme to stabilize pure states in the quantum system and employ an effective Hamiltonian method for the quantum master equation to elaborate on the nature of stabilizable states and the conditions under which state purification can be achieved. The state engineering within the quantum feedback scheme is shown to be linked with the solution of an inverse eigenvalue problem. Two applications of the feedback scheme are presented in detail: (i) stabilization of delocalized pure states in a single charge qubit and (ii) entanglement stabilization in two coupled charge qubits. In the latter example we demonstrate the stabilization of a maximally entangled Bell state for certain detector positions and local feedback operations.Comment: 23 pages, 6 figures, to be published by New Journal of Physics (2013

Josephson dynamics for coupled polariton modes under the atom-field interaction in the cavity

We consider a new approach to the problem of Bose-Einstein condensation (BEC) of polaritons for atom-field interaction under the strong coupling regime in the cavity. We investigate the dynamics of two macroscopically populated polariton modes corresponding to the upper and lower branch energy states coupled via Kerr-like nonlinearity of atomic medium. We found out the dispersion relations for new type of collective excitations in the system under consideration. Various temporal regimes like linear (nonlinear) Josephson transition and/or Rabi oscillations, macroscopic quantum self-trapping (MQST) dynamics for population imbalance of polariton modes are predicted. We also examine the switching properties for time-averaged population imbalance depending on initial conditions, effective nonlinear parameter of atomic medium and kinetic energy of low-branch polaritons.Comment: 10 pages, 6 postscript figures, uses svjour.cl