6,735 research outputs found
Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions
We give explicit numerical values with 100 decimal digits for the Mertens
constant involved in the asymptotic formula for and, as a by-product, for the Meissel-Mertens constant
defined as , for , ...,
and .Comment: 12 pages, 6 table
The longest excursion of stochastic processes in nonequilibrium systems
We consider the excursions, i.e. the intervals between consecutive zeros, of
stochastic processes that arise in a variety of nonequilibrium systems and
study the temporal growth of the longest one l_{\max}(t) up to time t. For
smooth processes, we find a universal linear growth \simeq
Q_{\infty} t with a model dependent amplitude Q_\infty. In contrast, for
non-smooth processes with a persistence exponent \theta, we show that <
l_{\max}(t) > has a linear growth if \theta
\sim t^{1-\psi} if \theta > \theta_c. The amplitude Q_{\infty} and the exponent
\psi are novel quantities associated to nonequilibrium dynamics. These
behaviors are obtained by exact analytical calculations for renewal and
multiplicative processes and numerical simulations for other systems such as
the coarsening dynamics in Ising model as well as the diffusion equation with
random initial conditions.Comment: 4 pages,2 figure
More efficient Bell inequalities for Werner states
In this paper we study the nonlocal properties of two-qubit Werner states
parameterized by the visibility parameter 0<p<1. New family of Bell
inequalities are constructed which prove the two-qubit Werner states to be
nonlocal for the parameter range 0.7056<p<1. This is slightly wider than the
range 0.7071<p<1, corresponding to the violation of the
Clauser-Horne-Shimony-Holt (CHSH) inequality. This answers a question posed by
Gisin in the positive, i.e., there exist Bell inequalities which are more
efficient than the CHSH inequality in the sense that they are violated by a
wider range of two-qubit Werner states.Comment: 7 pages, 1 figur
Reconstruction of deglacial sea surface temperatures in the tropical Pacific from selective analysis of a fossil coral
The Sr/Ca of coral skeletons demonstrates potential as an indicator of sea surface temperatures (SSTs). However, the glacial-interglacial SST ranges predicted from Sr/Ca of fossil corals are usually higher than from other marine proxies. We observed infilling of secondary aragonite, characterised by high Sr/Ca ratios, along intraskeletal pores of a fossil coral from Papua New Guinea that grew during the penultimate deglaciation (130 +/- 2 ka). Selective microanalysis of unaltered areas of the fossil coral indicates that SSTs at similar to 130 ka were <= 1 degrees C cooler than at present in contrast with bulk measurements ( combining infilled and unaltered areas) which indicate a difference of 6-7 degrees C. The analysis of unaltered areas of fossil skeletons by microprobe techniques may offer a route to more accurate reconstruction of past SSTs.</p
Grothendieck's constant and local models for noisy entangled quantum states
We relate the nonlocal properties of noisy entangled states to Grothendieck's
constant, a mathematical constant appearing in Banach space theory. For
two-qubit Werner states \rho^W_p=p \proj{\psi^-}+(1-p){\one}/{4}, we show
that there is a local model for projective measurements if and only if , where is Grothendieck's constant of order 3. Known bounds
on prove the existence of this model at least for ,
quite close to the current region of Bell violation, . We
generalize this result to arbitrary quantum states.Comment: 6 pages, 1 figur
The spectrum of large powers of the Laplacian in bounded domains
We present exact results for the spectrum of the Nth power of the Laplacian
in a bounded domain. We begin with the one dimensional case and show that the
whole spectrum can be obtained in the limit of large N. We also show that it is
a useful numerical approach valid for any N. Finally, we discuss implications
of this work and present its possible extensions for non integer N and for 3D
Laplacian problems.Comment: 13 pages, 2 figure
Non-Perturbative One-Loop Effective Action for Electrodynamics in Curved Spacetime
In this paper we explicitly evaluate the one-loop effective action in four
dimensions for scalar and spinor fields under the influence of a strong,
covariantly constant, magnetic field in curved spacetime. In the framework of
zeta function regularization, we find the one-loop effective action to all
orders in the magnetic field up to linear terms in the Riemannian curvature. As
a particular case, we also obtain the one-loop effective action for massless
scalar and spinor fields. In this setting, we found that the vacuum energy of
charged spinors with small mass becomes very large due entirely by the
gravitational correction.Comment: LaTeX, 23 page
Exact Site Percolation Thresholds Using the Site-to-Bond and Star-Triangle Transformations
I construct a two-dimensional lattice on which the inhomogeneous site
percolation threshold is exactly calculable and use this result to find two
more lattices on which the site thresholds can be determined. The primary
lattice studied here, the ``martini lattice'', is a hexagonal lattice with
every second site transformed into a triangle. The site threshold of this
lattice is found to be , while the others have and
. This last solution suggests a possible approach to establishing
the bound for the hexagonal site threshold, . To derive these
results, I solve a correlated bond problem on the hexagonal lattice by use of
the star-triangle transformation and then, by a particular choice of
correlations, solve the site problem on the martini lattice.Comment: 12 pages, 10 figures. Submitted to Physical Review
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