45,598 research outputs found
Configurations, and parallelograms associated to centers of mass
The purpose of this article is to
\begin{enumerate}
\item define the -fold center of mass arrangement for points
in the plane,
\item give elementary properties of and
\item give consequences concerning the space of distinct points
in the plane, no four of which are the vertices of a parallelogram.
\end{enumerate}
The main result proven in this article is that the classical unordered
configuration of points in the plane is not a retract up to homotopy of the
space of unordered distinct points in the plane, no four of which are the
vertices of a parallelogram. The proof below is homotopy theoretic without an
explicit computation of the homology of these spaces.
In addition, a second, speculative part of this article arises from the
failure of these methods in the case of odd primes . This failure gives rise
to a candidate for the localization at odd primes of the double loop space
of an odd sphere obtained from the -fold center of mass arrangement.
Potential consequences are listed.Comment: 11 page
Thermal effects on lattice strain in hcp Fe under pressure
We compute the c/a lattice strain versus temperature for nonmagnetic hcp iron
at high pressures using both first-principles linear response quasiharmonic
calculations based on the full potential linear-muffin-tin-orbital (LMTO)
method and the particle-in-cell (PIC) model for the vibrational partition
function using a tight-binding total-energy method. The tight-binding model
shows excellent agreement with the all-electron LMTO method. When hcp structure
is stable, the calculated geometric mean frequency and Helmholtz free energy of
hcp Fe from PIC and linear response lattice dynamics agree very well, as does
the axial ratio as a function of temperature and pressure. On-site
anharmonicity proves to be small up to the melting temperature, and PIC gives a
good estimate of its sign and magnitude. At low pressures, hcp Fe becomes
dynamically unstable at large c/a ratios, and the PIC model might fail where
the structure approaches lattice instability. The PIC approximation describes
well the vibrational behavior away from the instability, and thus is a
reasonable approach to compute high temperature properties of materials. Our
results show significant differences from earlier PIC studies, which gave much
larger axial ratio increases with increasing temperature, or reported large
differences between PIC and lattice dynamics results.Comment: 9 figure
Eulerian Statistically Preserved Structures in Passive Scalar Advection
We analyze numerically the time-dependent linear operators that govern the
dynamics of Eulerian correlation functions of a decaying passive scalar
advected by a stationary, forced 2-dimensional Navier-Stokes turbulence. We
show how to naturally discuss the dynamics in terms of effective compact
operators that display Eulerian Statistically Preserved Structures which
determine the anomalous scaling of the correlation functions. In passing we
point out a bonus of the present approach, in providing analytic predictions
for the time-dependent correlation functions in decaying turbulent transport.Comment: 10 pages, 10 figures. Submitted to Phys. Rev.
On the Tomography of Networks and Multicast Trees
In this paper we model the tomography of scale free networks by studying the
structure of layers around an arbitrary network node. We find, both
analytically and empirically, that the distance distribution of all nodes from
a specific network node consists of two regimes. The first is characterized by
rapid growth, and the second decays exponentially. We also show that the nodes
degree distribution at each layer is a power law with an exponential cut-off.
We obtain similar results for the layers surrounding the root of multicast
trees cut from such networks, as well as the Internet. All of our results were
obtained both analytically and on empirical Interenet data
Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems: II. Dipole-dipole versus current-current correlations
Based on Takayama-Lin-Liu-Maki model, analytical expressions for the
third-harmonic generation, DC Kerr effect, DC-induced second harmonic optical
Kerr effect, optical Kerr effect or intensity-dependent index of refraction and
DC-electric-field-induced optical rectification are derived under the static
current-current() correlation for one-dimensional infinite chains. The
results of hyperpolarizabilities under correlation are then compared
with those obtained using the dipole-dipole () correlation. The comparison
shows that the conventional correlation, albeit quite successful for
the linear case, is incorrect for studying the nonlinear optical properties of
periodic systems.Comment: 11 pages, 5 figure
Meanfield treatment of Bragg scattering from a Bose-Einstein condensate
A unified semiclassical treatment of Bragg scattering from Bose-Einstein
condensates is presented. The formalism is based on the Gross-Pitaevskii
equation driven by classical light fields far detuned from atomic resonance. An
approximate analytic solution is obtained and provides quantitative
understanding of the atomic momentum state oscillations, as well as a simple
expression for the momentum linewidth of the scattering process. The validity
regime of the analytic solution is derived, and tested by three dimensional
cylindrically symmetric numerical simulations.Comment: 21 pages, 10 figures. Minor changes made to documen
Polarization entanglement visibility of photon pairs emitted by a quantum dot embedded in a microcavity
We study the photon emission from a quantum dot embedded in a microcavity.
Incoherent pumping of its excitons and biexciton provokes the emission of leaky
and cavity modes. By solving a master equation we obtain the correlation
functions required to compute the spectrum and the relative efficiency among
the emission of pairs and single photons. A quantum regime appears for low
pumping and large rate of emission. By means of a post-selection process, a two
beams experiment with different linear polarizations could be performed
producing a large polarization entanglement visibility precisely in the quantum
regime.Comment: 13 pages and 6 figure
One-mirror Fabry-Perot and one-slit Young interferometry
We describe a new and distinctive interferometry in which a probe particle
scatters off a superposition of locations of a single free target particle. In
one dimension, probe particles incident on superposed locations of a single
"mirror" can interfere as if in a Fabry-Perot interferometer; in two
dimensions, probe particles scattering off superposed locations of a single
"slit" can interfere as if in a two-slit Young interferometer. The condition
for interference is loss of orthogonality of the target states and reduces, in
simple examples, to transfer of orthogonality from target to probe states. We
analyze experimental parameters and conditions necessary for interference to be
observed.Comment: 5 pages, 2 figures, RevTeX, submitted to PR
Comment on ``Consistent Sets Yield Contrary Inferences in Quantum Theory''
In a recent paper Kent has pointed out that in consistent histories quantum
theory it is possible, given initial and final states, to construct two
different consistent families of histories, in each of which there is a
proposition that can be inferred with probability one, and such that the
projectors representing these two propositions are mutually orthogonal. In this
note we stress that, according to the rules of consistent history reasoning two
such propositions are not contrary in the usual logical sense namely, that one
can infer that if one is true then the other is false, and both could be false.
No single consistent family contains both propositions, together with the
initial and final states, and hence the propositions cannot be logically
compared. Consistent histories quantum theory is logically consistent,
consistent with experiment as far as is known, consistent with the usual
quantum predictions for measurements, and applicable to the most general
physical systems. It may not be the only theory with these properties, but in
our opinion, it is the most promising among present possibilities.Comment: 2pages, uses REVTEX 3.
- …