76,205 research outputs found
Nonresonance conditions for arrangements
We prove a vanishing theorem for the cohomology of the complement of a
complex hyperplane arrangement with coefficients in a complex local system.
This result is compared with other vanishing theorems, and used to study Milnor
fibers of line arrangements, and hypersurface arrangements.Comment: LaTeX, 10 page
Proof of some asymptotic results for a model equation for low Reynolds number flow
A two-point boundary value problem in the interval [ε, ∞], ε > 0 is studied. The problem contains additional parameters α ≥ 0, β ≥ 0, 0 ≤ U 0; for α = 0 an explicit construction shows that no solution exists unless k > 1. A special method is used to show uniqueness. For ε ↓ 0, k ≥ 1, various results had previously been obtained by the method of matched asymptotic expansions. Examples of these results are verified rigorously using the integral representation. For k < 1, the problem is shown not to be a layer-type problem, a fact previously demonstrated explicitly for k = 0. If k is an integer ≥ 0 the intuitive understanding of the problem is aided by regarding it as spherically symmetric in k + 1 dimensions. In the present study, however, k may be any real number, even negative
Microscopic chaos from Brownian motion?
A recent experiment on Brownian motion has been interpreted to exhibit direct
evidence for microscopic chaos. In this note we demonstrate that virtually
identical results can be obtained numerically using a manifestly
microscopically nonchaotic system.Comment: 3 pages, 1 figure, Comment on P. Gaspard et al, Nature vol 394, 865
(1998); rewritten in a more popular styl
A Probabilistic proof of the breakdown of Besov regularity in -shaped domains
{We provide a probabilistic approach in order to investigate the smoothness
of the solution to the Poisson and Dirichlet problems in -shaped domains. In
particular, we obtain (probabilistic) integral representations for the
solution. We also recover Grisvard's classic result on the angle-dependent
breakdown of the regularity of the solution measured in a Besov scale
Comparing persistence diagrams through complex vectors
The natural pseudo-distance of spaces endowed with filtering functions is
precious for shape classification and retrieval; its optimal estimate coming
from persistence diagrams is the bottleneck distance, which unfortunately
suffers from combinatorial explosion. A possible algebraic representation of
persistence diagrams is offered by complex polynomials; since far polynomials
represent far persistence diagrams, a fast comparison of the coefficient
vectors can reduce the size of the database to be classified by the bottleneck
distance. This article explores experimentally three transformations from
diagrams to polynomials and three distances between the complex vectors of
coefficients.Comment: 11 pages, 4 figures, 2 table
Star formation in Carina OB1: Observations of a giant molecular cloud associated with the eta Carinae Nebula
A giant molecular cloud associated with the eta Carinae nebula was fully mapped in CO with the Columbia Millimeter-Wave Telescope at Cerro Tololo. The cloud comples has a mass of roughly 700,000 solar mass and extends about 140 pc along the Galactic plane, with the giant Carina HII region situated at one end of the complex. Clear evidence of interaction between the HII region and the molecular cloud is found in the relative motions of the ionized gas, the molecular gas, and the dust; simple energy and momentum considerations suggest that the HII region is responsible for the observed motion of a cloud fragment. The molecular cloud complex appears to be the parent material of the entire Car OB1 Association which, in addition to the young clusters in the Carine nebula, includes the generally older cluster NGC 3325, NGC 3293, and IC 2581. The overall star formation efficiency in the cloud complex is estimated to be approximately 0.02
Distillation of GHZ states by selective information manipulation
Methods for distilling maximally entangled tripartite (GHZ) states from
arbitrary entangled tripartite pure states are described. These techniques work
for virtually any input state. Each technique has two stages which we call
primary and secondary distillation. Primary distillation produces a GHZ state
with some probability, so that when applied to an ensemble of systems, a
certain percentage is discarded. Secondary distillation produces further GHZs
from the discarded systems. These protocols are developed with the help of an
approach to quantum information theory based on absolutely selective
information, which has other potential applications.Comment: minor corrections, especially of some numerical values; conclusions
unaffecte
The information entropy of quantum mechanical states
It is well known that a Shannon based definition of information entropy leads
in the classical case to the Boltzmann entropy. It is tempting to regard the
Von Neumann entropy as the corresponding quantum mechanical definition. But the
latter is problematic from quantum information point of view. Consequently we
introduce a new definition of entropy that reflects the inherent uncertainty of
quantum mechanical states. We derive for it an explicit expression, and discuss
some of its general properties. We distinguish between the minimum uncertainty
entropy of pure states, and the excess statistical entropy of mixtures.Comment: 7 pages, 1 figur
Noncovariant gauge fixing in the quantum Dirac field theory of atoms and molecules
Starting from the Weyl gauge formulation of quantum electrodynamics (QED),
the formalism of quantum-mechanical gauge fixing is extended using techniques
from nonrelativistic QED. This involves expressing the redundant gauge degrees
of freedom through an arbitrary functional of the gauge-invariant transverse
degrees of freedom. Particular choices of functional can be made to yield the
Coulomb gauge and Poincar\'{e} gauge representations. The Hamiltonian we derive
therefore serves as a good starting point for the description of atoms and
molecules by means of a relativistic Dirac field. We discuss important
implications for the ontology of noncovariant canonical QED due to the gauge
freedom that remains present in our formulation.Comment: 8 pages, 0 figure
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