69,024 research outputs found
Quadrature domains and kernel function zipping
It is proved that quadrature domains are ubiquitous in a very strong sense in
the realm of smoothly bounded multiply connected domains in the plane. In fact,
they are so dense that one might as well assume that any given smooth domain
one is dealing with is a quadrature domain, and this allows access to a host of
strong conditions on the classical kernel functions associated to the domain.
Following this string of ideas leads to the discovery that the Bergman kernel
can be zipped down to a strikingly small data set. It is also proved that the
kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati
Comment on "Separability of quantum states and the violation of Bell-type inequalities"
The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that
separable states can violate classical probabilistic constraints is based on a
misleading definition of classicality, which is much narrower than Bell's
concept of local hidden variables. In a Bell type setting the notion of
classicality used by Loubenets corresponds to the assumption of perfect
correlations if the same observable is measured on both sides. While it is
obvious that most separable states do not satisfy this assumption, this does
not constitute "non-classical" behaviour in any usual sense of the word.Comment: 1 page, accepted by Phys. Rev.
Submerged dunes and breakwater embayments mapped using wave inversions of shore-mounted marine X-Band radar data
Surveying very shallow coastal areas, particularly around
coastal defences, can be a logistically difficult and time
consuming process. A marine-radar based bathymetry mapping technique has been used to remotely map the embayments around a series of shore-parallel breakwaters at Sea Palling on the south east coast of England during the
LEACOAST2 project. The duration of the deployment spanned over 2 years, with the aim of observing any evolution of bathymetric features over that timescale while providing a clear indication of the spatial variability of wave and current patterns contributing to such evolution. The embayments generated by the shore parallel breakwaters at that site are resolved and a field of subtidal dunes with a wavelength of the order of 200m and amplitude around 1m located in approximately 6-10m of water were within the radar field of view and are evident in the remotely sensed bathymetry. Comparisons between bathymetric data obtained using conventional survey techniques and the radar based technique are presented together with measurements of tidal currents mapped using the same remote sensing method and compared with ADCP data during a storm even
Not throwing out the baby with the bathwater: Bell's condition of local causality mathematically 'sharp and clean'
The starting point of the present paper is Bell's notion of local causality
and his own sharpening of it so as to provide for mathematical formalisation.
Starting with Norsen's (2007, 2009) analysis of this formalisation, it is
subjected to a critique that reveals two crucial aspects that have so far not
been properly taken into account. These are (i) the correct understanding of
the notions of sufficiency, completeness and redundancy involved; and (ii) the
fact that the apparatus settings and measurement outcomes have very different
theoretical roles in the candidate theories under study. Both aspects are not
adequately incorporated in the standard formalisation, and we will therefore do
so. The upshot of our analysis is a more detailed, sharp and clean mathematical
expression of the condition of local causality. A preliminary analysis of the
repercussions of our proposal shows that it is able to locate exactly where and
how the notions of locality and causality are involved in formalising Bell's
condition of local causality.Comment: 14 pages. To be published in PSE volume "Explanation, Prediction, and
Confirmation", edited by Dieks, et a
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
J.S. Bell's Concept of Local Causality
John Stewart Bell's famous 1964 theorem is widely regarded as one of the most
important developments in the foundations of physics. It has even been
described as "the most profound discovery of science." Yet even as we approach
the 50th anniversary of Bell's discovery, its meaning and implications remain
controversial. Many textbooks and commentators report that Bell's theorem
refutes the possibility (suggested especially by Einstein, Podolsky, and Rosen
in 1935) of supplementing ordinary quantum theory with additional ("hidden")
variables that might restore determinism and/or some notion of an
observer-independent reality. On this view, Bell's theorem supports the
orthodox Copenhagen interpretation. Bell's own view of his theorem, however,
was quite different. He instead took the theorem as establishing an "essential
conflict" between the now well-tested empirical predictions of quantum theory
and relativistic \emph{local causality}. The goal of the present paper is, in
general, to make Bell's own views more widely known and, in particular, to
explain in detail Bell's little-known mathematical formulation of the concept
of relativistic local causality on which his theorem rests. We thus collect and
organize many of Bell's crucial statements on these topics, which are scattered
throughout his writings, into a self-contained, pedagogical discussion
including elaborations of the concepts "beable", "completeness", and
"causality" which figure in the formulation. We also show how local causality
(as formulated by Bell) can be used to derive an empirically testable Bell-type
inequality, and how it can be used to recapitulate the EPR argument.Comment: 19 pages, 4 figure
Quantum interference and non-locality of independent photons from disparate sources
We quantitatively investigate the non-classicality and non-locality of a
whole new class of mixed disparate quantum and semiquantum photon sources at
the quantum-classical boundary. The latter include photon added thermal and
photon added coherent sources, experimentally investigated recently by Zavatta
et al. [Phys. Rev. Lett. 103, 140406 (2009)]. The key quantity in our
investigations is the visibility of the corresponding photon-photon correlation
function. We present explicit results on the violations of the Cauchy-Schwarz
inequality - which is a measure of nonclassicality - as well as of Bell-type
inequalities.Comment: 9 pages, 3 figure
Monogamy of Bell's inequality violations in non-signaling theories
We derive monogamy relations (tradeoffs) between strengths of violations of
Bell's inequalities from the non-signaling condition. Our result applies to
general Bell inequalities with an arbitrary large number of partners, outcomes
and measurement settings. The method is simple, efficient and does not require
linear programming. The results are used to derive optimal fidelity for
asymmetric cloning in nonsignaling theories.Comment: 4 pages, 2 figures, published versio
Class of bipartite quantum states satisfying the original Bell inequality
In a general setting, we introduce a new bipartite state property sufficient
for the validity of the perfect correlation form of the original Bell
inequality for any three bounded quantum observables. A bipartite quantum state
with this property does not necessarily exhibit perfect correlations. The class
of bipartite states specified by this property includes both separable and
nonseparable states. We prove analytically that, for any dimension d>2, every
Werner state, separable or nonseparable, belongs to this class.Comment: 6 pages, v.2: one reference added, the statement on Werner states
essentially extended; v.3: details of proofs inserte
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