46,332 research outputs found
Bell's theorem as a signature of nonlocality: a classical counterexample
For a system composed of two particles Bell's theorem asserts that averages
of physical quantities determined from local variables must conform to a family
of inequalities. In this work we show that a classical model containing a local
probabilistic interaction in the measurement process can lead to a violation of
the Bell inequalities. We first introduce two-particle phase-space
distributions in classical mechanics constructed to be the analogs of quantum
mechanical angular momentum eigenstates. These distributions are then employed
in four schemes characterized by different types of detectors measuring the
angular momenta. When the model includes an interaction between the detector
and the measured particle leading to ensemble dependencies, the relevant Bell
inequalities are violated if total angular momentum is required to be
conserved. The violation is explained by identifying assumptions made in the
derivation of Bell's theorem that are not fulfilled by the model. These
assumptions will be argued to be too restrictive to see in the violation of the
Bell inequalities a faithful signature of nonlocality.Comment: Extended manuscript. Significant change
The Identity Correspondence Problem and its Applications
In this paper we study several closely related fundamental problems for words
and matrices. First, we introduce the Identity Correspondence Problem (ICP):
whether a finite set of pairs of words (over a group alphabet) can generate an
identity pair by a sequence of concatenations. We prove that ICP is undecidable
by a reduction of Post's Correspondence Problem via several new encoding
techniques.
In the second part of the paper we use ICP to answer a long standing open
problem concerning matrix semigroups: "Is it decidable for a finitely generated
semigroup S of square integral matrices whether or not the identity matrix
belongs to S?". We show that the problem is undecidable starting from dimension
four even when the number of matrices in the generator is 48. From this fact,
we can immediately derive that the fundamental problem of whether a finite set
of matrices generates a group is also undecidable. We also answer several
question for matrices over different number fields. Apart from the application
to matrix problems, we believe that the Identity Correspondence Problem will
also be useful in identifying new areas of undecidable problems in abstract
algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the
published journal version of this article, see footnote 3 on page 1
Hardy's proof of nonlocality in the presence of noise
We extend the validity of Hardy's nonlocality without inequalities proof to
cover the case of special one-parameter classes of non-pure statistical
operators. These mixed states are obtained by mixing the Hardy states with a
completely chaotic noise or with a colored noise and they represent a realistic
description of imperfect preparation processes of (pure) Hardy states in
nonlocality experiments. Within such a framework we are able to exhibit a
precise range of values of the parameter measuring the noise affecting the
non-optimal preparation of an arbitrary Hardy state, for which it is still
possible to put into evidence genuine nonlocal effects. Equivalently, our work
exhibits particular classes of bipartite mixed states whose constituents do not
admit any local and deterministic hidden variable model reproducing the quantum
mechanical predictions.Comment: 9 pages, 2 figures, RevTex, revised versio
Spatial Economic Analysis in Data-Rich Environments
Controlling for spatial effects in micro-economic studies of consumer and producer behavior necessitates a range of analytical modifications ranging from modest changes in data collection and the definition of variables to dramatic changes in the modeling of consumer and producer decision-making. This paper discusses conceptual, empirical, and data issues involved in modeling the spatial aspects of economic behavior in data rich environments. Attention is given to established and emerging agricultural economic applications of spatial data and spatial econometric methods at the micro-scale. Recent applications of individual and household data are featured, including models of land-use change at the urban-rural interface, agricultural land values, and technological change and technology adoption.Research Methods/ Statistical Methods, C21, Q10, Q12, Q15, Q56,
Building the Infrastructure: The Effects of Role Identification Behaviors on Team Cognition Development and Performance
The primary purpose of this study was to extend theory and research regarding the emergence of mental models and transactive memory in teams. Utilizing Kozlowski et al.’s (1999) model of team compilation, we examine the effect of role identification behaviors and argue that such behaviors represent the initial building blocks of team cognition during the role compilation phase of team development. We then hypothesized that team mental models and transactive memory would convey the effects of these behaviors onto team performance in the team compilation phase of development. Results from 60 teams working on a command and control simulation supported our hypotheses
The Dynamical Mordell-Lang problem
Let X be a Noetherian space, let f be a continuous self-map on X, let Y be a
closed subset of X, and let x be a point on X. We show that the set S
consisting of all nonnegative integers n such that f^n(x) is in Y is a union of
at most finitely many arithmetic progressions along with a set of Banach
density zero. In particular, we obtain that given any quasi-projective variety
X, any rational self-map map f on X, any subvariety Y of X, and any point x in
X whose orbit under f is in the domain of definition for f, the set S is a
finite union of arithmetic progressions together with a set of Banach density
zero. We prove a similar result for the backward orbit of a point
Loophole-free Bell's experiment and two-photon all-versus-nothing violation of local realism
We introduce an all-versus-nothing proof of impossibility of
Einstein-Podolsky-Rosen's local elements of reality for two photons entangled
both in polarization and path degrees of freedom, which leads to a Bell's
inequality where the classical bound is 8 and the quantum prediction is 16. A
simple estimation of the detection efficiency required to close the detection
loophole using this proof gives eta > 0.69. This efficiency is lower than that
required for previous proposals.Comment: REVTeX4, 4 page
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