835 research outputs found
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 of a quantum wire in the limit of one occupied
subband. At zero temperature, a Tomonaga-Luttinger-like renormalization of
to a value slightly larger than 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, OsN and OsO are
mechanically stable. In particular OsN has the highest bulk modulus of
360.7 GPa. Both the band structure and density of states show that the new
phase of OsN 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 -th moment of the
probability density scales like in dimensions. The
return probability scales like , with the generalized
dimension of the participation ratio . For long times and short distances
the probability density of the wave packet shows power law scaling
. 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
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