12,073 research outputs found
The Source Size Dependence on the M_hadron Applying Fermi and Bose Statistics and I-Spin Invariance
The emission volume sizes of pions and Kaons, r_{\pi^\pm \pi^\pm} and
r_{K^\pm K^\pm}, measured in the hadronic Z^0 decays via the Bose-Einstein
Correlations (BEC), and the recent measurements of r_{\Lambda\Lambda} obtained
by through the Pauli exclusion principle are used to study the r dependence on
the hadron mass. A clear r_{\pi^\pm \pi^\pm} > r_{K^\pm K^\pm} > r_{\Lambda
\Lambda} hierarchy is observed which seems to disagree with the basic string
(LUND) model expectation. An adequate description of r(m) is obtained via the
Heisenberg uncertainty relations and also by Local Parton Hadron Duality
approach using a general QCD potential. These lead to a relation of the type
r(m) ~ Constant/sqrt{m}.
The present lack of knowledge on the f_o(980) decay rate to the K^0\bar{K}^0
channel prohibits the use of the r_{K^0_SK^0_S} in the r(m) analysis. The use
of a generalised BEC and I-spin invariance, which predicts an BEC enhancement
also in the K^{\pm}K^0 and \pi^{\pm}\pi^0 systems, should in the future help to
include the r_{K^0_SK^0_S} in the r(m) analysis.Comment: 7 pages, 4 figures, Based on an invited talk given by G. Alexander at
the XXIX Int. Symp. on Multiparticle Dynamics, 9-13 August 1999, Providence
RI, USA. (to be published in the proceedings of this conference
Characteristic varieties of arrangements
The k-th Fitting ideal of the Alexander invariant B of an arrangement A of n
complex hyperplanes defines a characteristic subvariety, V_k(A), of the complex
algebraic n-torus. In the combinatorially determined case where B decomposes as
a direct sum of local Alexander invariants, we obtain a complete description of
V_k(A). For any arrangement A, we show that the tangent cone at the identity of
this variety coincides with R^1_k(A), one of the cohomology support loci of the
Orlik-Solomon algebra. Using work of Arapura and Libgober, we conclude that all
positive-dimensional components of V_k(A) are combinatorially determined, and
that R^1_k(A) is the union of a subspace arrangement in C^n, thereby resolving
a conjecture of Falk. We use these results to study the reflection arrangements
associated to monomial groups.Comment: LaTeX2e, 20 pages. A reference to Libgober's recent work in
math.AG/9801070 is added. Several points are clarified, a new example is
include
Alexander Invariants of Complex Hyperplane Arrangements
Let A be an arrangement of complex hyperplanes. The fundamental group of the
complement of A is determined by a braid monodromy homomorphism from a finitely
generated free group to the pure braid group. Using the Gassner representation
of the pure braid group, we find an explicit presentation for the Alexander
invariant of A. From this presentation, we obtain combinatorial lower bounds
for the ranks of the Chen groups of A. We also provide a combinatorial
criterion for when these lower bounds are attained.Comment: 26 pages; LaTeX2e with amscd, amssymb package
Semilinear response for the heating rate of cold atoms in vibrating traps
The calculation of the heating rate of cold atoms in vibrating traps requires
a theory that goes beyond the Kubo linear response formulation. If a strong
"quantum chaos" assumption does not hold, the analysis of transitions shows
similarities with a percolation problem in energy space. We show how the
texture and the sparsity of the perturbation matrix, as determined by the
geometry of the system, dictate the result. An improved sparse random matrix
model is introduced: it captures the essential ingredients of the problem, and
leads to a generalized variable range hopping picture.Comment: 6 pages, 6 figures, improved version to be published in Europhysics
Letter
The boundary manifold of a complex line arrangement
We study the topology of the boundary manifold of a line arrangement in CP^2,
with emphasis on the fundamental group G and associated invariants. We
determine the Alexander polynomial Delta(G), and more generally, the twisted
Alexander polynomial associated to the abelianization of G and an arbitrary
complex representation. We give an explicit description of the unit ball in the
Alexander norm, and use it to analyze certain Bieri-Neumann-Strebel invariants
of G. From the Alexander polynomial, we also obtain a complete description of
the first characteristic variety of G. Comparing this with the corresponding
resonance variety of the cohomology ring of G enables us to characterize those
arrangements for which the boundary manifold is formal.Comment: This is the version published by Geometry & Topology Monographs on 22
February 200
Translated tori in the characteristic varieties of complex hyperplane arrangements
We give examples of complex hyperplane arrangements for which the top
characteristic variety contains positive-dimensional irreducible components
that do not pass through the origin of the character torus. These examples
answer several questions of Libgober and Yuzvinsky. As an application, we
exhibit a pair of arrangements for which the resonance varieties of the
Orlik-Solomon algebra are (abstractly) isomorphic, yet whose characteristic
varieties are not isomorphic. The difference comes from translated components,
which are not detected by the tangent cone at the origin.Comment: Revised and expanded; 16 pages, 10 figures; to appear in Topology and
its Application
A central limit theorem for the sample autocorrelations of a L\'evy driven continuous time moving average process
In this article we consider L\'evy driven continuous time moving average
processes observed on a lattice, which are stationary time series. We show
asymptotic normality of the sample mean, the sample autocovariances and the
sample autocorrelations. A comparison with the classical setting of discrete
moving average time series shows that in the last case a correction term should
be added to the classical Bartlett formula that yields the asymptotic variance.
An application to the asymptotic normality of the estimator of the Hurst
exponent of fractional L\'evy processes is also deduced from these results
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