1,157,708 research outputs found
Average distance in a hierarchical scale-free network: an exact solution
Various real systems simultaneously exhibit scale-free and hierarchical
structure. In this paper, we study analytically average distance in a
deterministic scale-free network with hierarchical organization. Using a
recursive method based on the network construction, we determine explicitly the
average distance, obtaining an exact expression for it, which is confirmed by
extensive numerical calculations. The obtained rigorous solution shows that the
average distance grows logarithmically with the network order (number of nodes
in the network). We exhibit the similarity and dissimilarity in average
distance between the network under consideration and some previously studied
networks, including random networks and other deterministic networks. On the
basis of the comparison, we argue that the logarithmic scaling of average
distance with network order could be a generic feature of deterministic
scale-free networks.Comment: Definitive version published in Journal of Statistical Mechanic
The Bekenstein-Hawking Entropy of Higher-Dimensional Rotating Black Holes
A black hole can be regarded as a thermodynamic system described by a grand
canonical ensemble. In this paper, we study the Bekenstein-Hawking entropy of
higher-dimensional rotating black holes using the Euclidean path-integral
method of Gibbons and Hawking. We give a general proof demonstrating that
ignoring quantum corrections, the Bekenstein-Hawking entropy is equal to
one-fourth of its horizon area for general higher-dimensional rotating black
holes.Comment: 9 pages, Latex, v2: arxiv-id for the references supplemented, v3:
accepted for publication by Progress of Theoretical Physic
Variational separable expansion scheme for two-body Coulomb-scattering problems
We present a separable expansion approximation method for Coulomb-like
potentials which is based on Schwinger variational principle and uses
Coulomb-Sturmian functions as basis states. The new scheme provides faster
convergence with respect to our formerly used non-variational approach.Comment: some typos correcte
Fibre bundle formulation of nonrelativistic quantum mechanics. IV. Mixed states and evolution transport's curvature
We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. It's evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
The present fourth part of this series is devoted mainly to the fibre bundle
description of mixed quantum states. We show that to the conventional density
operator there corresponds a unique density morphism (along paths) for which
the corresponding equations of motion are derived. It is also investigated the
bundle description of mixed quantum states in the different pictures of motion.
We calculate the curvature of the evolution transport and prove that it is
curvature free iff the values of the Hamiltonian operator at different moments
commute.Comment: 14 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and
amsfonts are required. Minor style changes, a problem with the bibliography
is corrected. Continuation of quant-ph/9803083, quant-ph/9803084,
quant-ph/9804062 and quant-ph/9806046. For continuation of the series and
related papers, view http://www.inrne.bas.bg/mathmod/bozhome
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