21,629 research outputs found
Input-output relations for multiport ring cavities
Quantum input-output relations for a generic -port ring cavity are
obtained by modeling the ring as a cascade of interlinked beam splitters.
Cavity response to a beam impinging on one port is studied as a function of the
beam-splitter reflectivities and the internal phase-shifts. Interferometric
sensitivity and stability are analyzed as a function of the number of ports.Comment: 6 pages, 5 figures (low-res
Slow relaxation in the Ising model on a small-world network with strong long-range interactions
We consider the Ising model on a small-world network, where the long-range
interaction strength is in general different from the local interaction
strength , and examine its relaxation behaviors as well as phase
transitions. As is raised from zero, the critical temperature also
increases, manifesting contributions of long-range interactions to ordering.
However, it becomes saturated eventually at large values of and the
system is found to display very slow relaxation, revealing that ordering
dynamics is inhibited rather than facilitated by strong long-range
interactions. To circumvent this problem, we propose a modified updating
algorithm in Monte Carlo simulations, assisting the system to reach equilibrium
quickly.Comment: 5 pages, 5 figure
Are better conducting molecules more rigid?
We investigate the electronic origin of the bending stiffness of conducting
molecules. It is found that the bending stiffness associated with electronic
motion, which we refer to as electro-stiffness, , is governed by
the molecular orbital overlap and the gap width between HOMO and LUMO
levels, and behaves as . To study the
effect of doping, we analyze the electron filling-fraction dependence on
and show that doped molecules are more flexible. In addition, to
estimate the contribution of to the total stiffness, we consider
molecules under a voltage bias, and study the length contraction ratio as a
function of the voltage. The molecules are shown to be contracted or dilated,
with increasing nonlinearly with the applied bias
Problems with Fitting to the Power-Law Distribution
This short communication uses a simple experiment to show that fitting to a
power law distribution by using graphical methods based on linear fit on the
log-log scale is biased and inaccurate. It shows that using maximum likelihood
estimation (MLE) is far more robust. Finally, it presents a new table for
performing the Kolmogorov-Smirnof test for goodness-of-fit tailored to
power-law distributions in which the power-law exponent is estimated using MLE.
The techniques presented here will advance the application of complex network
theory by allowing reliable estimation of power-law models from data and
further allowing quantitative assessment of goodness-of-fit of proposed
power-law models to empirical data.Comment: 4 pages, 1 figure, 2 table
Monogamy and polygamy for multi-qubit entanglement using R\'enyi entropy
Using R\'enyi- entropy to quantify bipartite entanglement, we prove
monogamy of entanglement in multi-qubit systems for . We also
conjecture a polygamy inequality of multi-qubit entanglement with strong
numerical evidence for with
.Comment: 19 pages, 2 figure
An evolving network model with community structure
Many social and biological networks consist of communities—groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting community structures in real-world complex networks. In this paper, we propose an evolving network model which exhibits community structure. The network model is based on the inner-community preferential attachment and inter-community preferential attachment mechanisms. The degree distributions of this network model are analysed based on a mean-field method. Theoretical results and numerical simulations indicate that this network model has community structure and scale-free properties
Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals
The quasi-unit cell picture describes the atomic structure of quasicrystals
in terms of a single, repeating cluster which overlaps neighbors according to
specific overlap rules. In this paper, we discuss the precise relationship
between a general atomic decoration in the quasi-unit cell picture atomic
decorations in the Penrose tiling and in related tiling pictures. Using these
relations, we obtain a simple, practical method for determining the density,
stoichiometry and symmetry of a quasicrystal based on the atomic decoration of
the quasi-unit cell taking proper account of the sharing of atoms between
clusters.Comment: 14 pages, 8 figure
The Rich Mid-Infrared Environments of Two Highly-Obscured X-ray Binaries: Spitzer Observations of IGR J16318-4848 and GX 301-2
We present the results of Spitzer mid-infrared spectroscopic observations of
two highly-obscured massive X-ray binaries: IGR J16318-4848 and GX301-2. Our
observations reveal for the first time the extremely rich mid-infrared
environments of this type of source, including multiple continuum emission
components (a hot component with T > 700 K and a warm component with T ~ 180 K)
with apparent silicate absorption features, numerous HI recombination lines,
many forbidden ionic lines of low ionization potentials, and pure rotational H2
lines. This indicates that both sources have hot and warm circumstellar dust,
ionized stellar winds, extended low-density ionized regions, and
photo-dissociated regions. It appears difficult to attribute the total optical
extinction of both sources to the hot and warm dust components, which suggests
that there could be an otherwise observable colder dust component responsible
for the most of the optical extinction and silicate absorption features. The
observed mid-infrared spectra are similar to those from Luminous Blue
Variables, indicating that the highly-obscured massive X-ray binaries may
represent a previously unknown evolutionary phase of X-ray binaries with
early-type optical companions. Our results highlight the importance and utility
of mid-infrared spectroscopy to investigate highly-obscured X-ray binaries.Comment: To appear in ApJ Letter
Condition numbers and scale free graphs
In this work we study the condition number of the least square matrix
corresponding to scale free networks. We compute a theoretical lower bound of
the condition number which proves that they are ill conditioned. Also, we
analyze several matrices from networks generated with the linear preferential
attachment model showing that it is very difficult to compute the power law
exponent by the least square method due to the severe lost of accuracy expected
from the corresponding condition numbers.Comment: Submitted to EP
Lattice dynamics and correlated atomic motion from the atomic pair distribution function
The mean-square relative displacements (MSRD) of atomic pair motions in
crystals are studied as a function of pair distance and temperature using the
atomic pair distribution function (PDF). The effects of the lattice vibrations
on the PDF peak widths are modelled using both a multi-parameter Born
von-Karman (BvK) force model and a single-parameter Debye model. These results
are compared to experimentally determined PDFs. We find that the near-neighbor
atomic motions are strongly correlated, and that the extent of this correlation
depends both on the interatomic interactions and crystal structure. These
results suggest that proper account of the lattice vibrational effects on the
PDF peak width is important in extracting information on static disorder in a
disordered system such as an alloy. Good agreement is obtained between the BvK
model calculations of PDF peak widths and the experimentally determined peak
widths. The Debye model successfully explains the average, though not detailed,
natures of the MSRD of atomic pair motion with just one parameter. Also the
temperature dependence of the Debye model largely agrees with the BvK model
predictions. Therefore, the Debye model provides a simple description of the
effects of lattice vibrations on the PDF peak widths.Comment: 9 pages, 11 figure
- …