1,944 research outputs found
A New Symmetric Expression of Weyl Ordering
For the creation operator \adag and the annihilation operator of a
harmonic oscillator, we consider Weyl ordering expression of (\adag a)^n and
obtain a new symmetric expression of Weyl ordering w.r.t. \adag a \equiv N
and a\adag =N+1 where is the number operator. Moreover, we interpret
intertwining formulas of various orderings in view of the difference theory.
Then we find that the noncommutative parameter corresponds to the increment of
the difference operator w.r.t. variable . Therefore, quantum
(noncommutative) calculations of harmonic oscillators are done by classical
(commutative) ones of the number operator by using the difference theory. As a
by-product, nontrivial relations including the Stirling number of the first
kind are also obtained.Comment: 15 pages, Latex2e, the title before replacement is "Orderings of
Operators in Quantum Physics", new proofs by using a difference operator
added, some references added, to appear in Modern Physics Letters
Subalgebras with Converging Star Products in Deformation Quantization: An Algebraic Construction for \complex \mbox{\LARGE P}^n
Based on a closed formula for a star product of Wick type on \CP^n, which
has been discovered in an earlier article of the authors, we explicitly
construct a subalgebra of the formal star-algebra (with coefficients contained
in the uniformly dense subspace of representative functions with respect to the
canonical action of the unitary group) that consists of {\em converging} power
series in the formal parameter, thereby giving an elementary algebraic proof of
a convergence result already obtained by Cahen, Gutt, and Rawnsley. In this
subalgebra the formal parameter can be substituted by a real number :
the resulting associative algebras are infinite-dimensional except for the case
, a positive integer, where they turn out to be isomorphic to
the finite-dimensional algebra of linear operators in the th energy
eigenspace of an isotropic harmonic oscillator with degrees of freedom.
Other examples like the -torus and the Poincar\'e disk are discussed.Comment: 16 pages, LaTeX with AMS Font
On the influence of time and space correlations on the next earthquake magnitude
A crucial point in the debate on feasibility of earthquake prediction is the
dependence of an earthquake magnitude from past seismicity. Indeed, whilst
clustering in time and space is widely accepted, much more questionable is the
existence of magnitude correlations. The standard approach generally assumes
that magnitudes are independent and therefore in principle unpredictable. Here
we show the existence of clustering in magnitude: earthquakes occur with higher
probability close in time, space and magnitude to previous events. More
precisely, the next earthquake tends to have a magnitude similar but smaller
than the previous one. A dynamical scaling relation between magnitude, time and
space distances reproduces the complex pattern of magnitude, spatial and
temporal correlations observed in experimental seismic catalogs.Comment: 4 Figure
Statistical mechanics of lossy compression for non-monotonic multilayer perceptrons
A lossy data compression scheme for uniformly biased Boolean messages is
investigated via statistical mechanics techniques. We utilize tree-like
committee machine (committee tree) and tree-like parity machine (parity tree)
whose transfer functions are non-monotonic. The scheme performance at the
infinite code length limit is analyzed using the replica method. Both committee
and parity treelike networks are shown to saturate the Shannon bound. The AT
stability of the Replica Symmetric solution is analyzed, and the tuning of the
non-monotonic transfer function is also discussed.Comment: 29 pages, 7 figure
Effect of Compton Scattering on the Electron Beam Dynamics at the ATF Damping Ring
Compton scattering provides one of the most promising scheme to obtain
polarized positrons for the next generation of -- colliders.
Moreover it is an attractive method to produce monochromatic high energy
polarized gammas for nuclear applications and X-rays for compact light sources.
In this framework a four-mirror Fabry-P\'erot cavity has been installed at the
Accelerator Test Facility (ATF - KEK, Tsukuba, Japan) and is used to produce an
intense flux of polarized gamma rays by Compton scattering
\cite{ipac-mightylaser}. For electrons at the ATF energy (1.28 GeV) Compton
scattering may result in a shorter lifetime due to the limited bucket
acceptance. We have implemented the effect of Compton scattering on a 2D
tracking code with a Monte-Carlo method. This code has been used to study the
longitudinal dynamics of the electron beam at the ATF damping ring, in
particular the evolution of the energy spread and the bunch length under
Compton scattering. The results obtained are presented and discussed. Possible
methods to observe the effect of Compton scattering on the ATF beam are
proposed
The Network of Epicenters of the Olami-Feder-Christensen Model of Earthquakes
We study the dynamics of the Olami-Feder-Christensen (OFC) model of
earthquakes, focusing on the behavior of sequences of epicenters regarded as a
growing complex network. Besides making a detailed and quantitative study of
the effects of the borders (the occurrence of epicenters is dominated by a
strong border effect which does not scale with system size), we examine the
degree distribution and the degree correlation of the graph. We detect sharp
differences between the conservative and nonconservative regimes of the model.
Removing border effects, the conservative regime exhibits a Poisson-like degree
statistics and is uncorrelated, while the nonconservative has a broad
power-law-like distribution of degrees (if the smallest events are ignored),
which reproduces the observed behavior of real earthquakes. In this regime the
graph has also a unusually strong degree correlation among the vertices with
higher degree, which is the result of the existence of temporary attractors for
the dynamics: as the system evolves, the epicenters concentrate increasingly on
fewer sites, exhibiting strong synchronization, but eventually spread again
over the lattice after a series of sufficiently large earthquakes. We propose
an analytical description of the dynamics of this growing network, considering
a Markov process network with hidden variables, which is able to account for
the mentioned properties.Comment: 9 pages, 10 figures. Smaller number of figures, and minor text
corrections and modifications. For version with full resolution images see
http://fig.if.usp.br/~tpeixoto/cond-mat-0602244.pd
Time dependent transformations in deformation quantization
We study the action of time dependent canonical and coordinate
transformations in phase space quantum mechanics. We extend the covariant
formulation of the theory by providing a formalism that is fully invariant
under both standard and time dependent coordinate transformations. This result
considerably enlarges the set of possible phase space representations of
quantum mechanics and makes it possible to construct a causal representation
for the distributional sector of Wigner quantum mechanics.Comment: 16 pages, to appear in the J. Math. Phy
Time-energy correlations in solar flare occurrence
The existence of time-energy correlations in flare occurrence is still an
open and much debated problem. This study addresses the question whether
statistically significant correlations are present between energies of
successive flares as well as energies and waiting times. We analyze the GOES
catalog with a statistical approach based on the comparison of the real catalog
with a reshuffled one where energies are decorrelated. This analysis reduces
the effect of background activity and is able to reveal the role of
obscuration. We show the existence of non-trivial correlations between waiting
times and energies, as well as between energies of subsequent flares. More
precisely, we find that flares close in time tend to have the second event with
large energy. Moreover, after large flares the flaring rate significantly
increases, together with the probability of other large flares. Results suggest
that correlations between energies and waiting times are a physical property
and not an effect of obscuration. These findings could give important
information on the mechanisms for energy storage and release in the solar
corona
Necessity to Measure PCBs and Organochlorine Pesticide Concentrations in Human Umbilical Cords for Fetal Exposure Assessment
Three types of tissue samplesâumbilical cord (UC), umbilical cord serum (CS), and maternal serum (MS)âhave often been used to assess fetal exposure to chemicals. In order to know the relationship of contamination between mothers and fetuses, we measured persistent chemicals in comparable sets of the three tissue samples. Also, we analyzed the association between the chemicals in maternal and fetal tissues to know which tissue is the best sample for fetal exposure assessment. On a wet basis, the chemical concentrations were of the order MS > CS > UC, except for some chemicals such as cis-chlordane and endosulfan. On a lipid basis, the concentrations in UC were nearly equal or often higher than in MS, but the concentrations in CS were usually lower than in others. Hexachlorocyclohexanes and penta-, hexa-, and heptachlorinated biphenyls showed an association between the concentrations in UC versus MS, and UC versus CS. These chemicals also showed high correlation coefficients between the chemical concentrations in UC of first babies and maternal age. These chemicals were closely related to each other when grouped on the basis of their concentrations using cluster analysis. In conclusion, we insist that UC is the best sample to assess fetal contamination status of persistent chemicals. There is a possibility that the assessment based on the contamination levels in CS result in an underestimation
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