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

Enterprise application reuse: Semantic discovery of business grid services

Web services have emerged as a prominent paradigm for the development of distributed software systems as they provide the potential for software to be modularized in a way that functionality can be described, discovered and deployed in a platform independent manner over a network (e.g., intranets, extranets and the Internet). This paper examines an extension of this paradigm to encompass ‘Grid Services’, which enables software capabilities to be recast with an operational focus and support a heterogeneous mix of business software and data, termed a Business Grid - "the grid of semantic services". The current industrial representation of services is predominantly syntactic however, lacking the fundamental semantic underpinnings required to fulfill the goals of any semantically-oriented Grid. Consequently, the use of semantic technology in support of business software heterogeneity is investigated as a likely tool to support a diverse and distributed software inventory and user. Service discovery architecture is therefore developed that is (a) distributed in form, (2) supports distributed service knowledge and (3) automatically extends service knowledge (as greater descriptive precision is inferred from the operating application system). This discovery engine is used to execute several real-word scenarios in order to develop and test a framework for engineering such grid service knowledge. The examples presented comprise software components taken from a group of Investment Banking systems. Resulting from the research is a framework for engineering servic

Nonclassical Nature of Dispersion Cancellation and Nonlocal Interferometry

Several recent papers have shown that some forms of dispersion cancellation have classical analogs and that some aspects of nonlocal two-photon interferometry are consistent with local realistic models. It is noted here that the classical analogs only apply to local dispersion cancellation experiments [A.M. Steinberg et al., Phys. Rev. Lett. 68, 2421 (1992)] and that nonlocal dispersion cancellation [J.D. Franson, Phys. Rev. A 45, 3126 (1992)] is inconsistent with any classical field theory and has no classical analog. The local models that have been suggested for two-photon interferometry are shown to be local but not realistic if the spatial extent of the interferometers is taken into account. It is the inability of classical models to describe all of the relevant aspects of these experiments that distinguishes between quantum and classical physics, which is also the case in Bell's inequality.Comment: 10 pages, 8 figures; minor revisions, to appear in Phys. Rev.

The Relativistically Spinning Charged Sphere

When the equatorial spin velocity, $v$, of a charged conducting sphere approaches $c$, the Lorentz force causes a remarkable rearrangement of the total charge $q$. Charge of that sign is confined to a narrow equatorial belt at latitudes $b \leqslant \sqrt{3} (1 - v^2/c^2)^{{1/2}}$ while charge of the opposite sign occupies most of the sphere's surface. The change in field structure is shown to be a growing contribution of the `magic' electromagnetic field of the charged Kerr-Newman black hole with Newton's G set to zero. The total charge within the narrow equatorial belt grows as $(1-v^2/c^2)^{-{1/4}}$ and tends to infinity as $v$ approaches $c$. The electromagnetic field, Poynting vector, field angular momentum and field energy are calculated for these configurations. Gyromagnetic ratio, g-factor and electromagnetic mass are illustrated in terms of a 19th Century electron model. Classical models with no spin had the small classical electron radius $e^2/mc^2\sim$ a hundredth of the Compton wavelength, but models with spin take that larger size but are so relativistically concentrated to the equator that most of their mass is electromagnetic. The method of images at inverse points of the sphere is shown to extend to charges at points with imaginary co-ordinates.Comment: 15 pages, 1figur

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

Experimenter's Freedom in Bell's Theorem and Quantum Cryptography

Bell's theorem states that no local realistic explanation of quantum mechanical predictions is possible, in which the experimenter has a freedom to choose between different measurement settings. Within a local realistic picture the violation of Bell's inequalities can only be understood if this freedom is denied. We determine the minimal degree to which the experimenter's freedom has to be abandoned, if one wants to keep such a picture and be in agreement with the experiment. Furthermore, the freedom in choosing experimental arrangements may be considered as a resource, since its lacking can be used by an eavesdropper to harm the security of quantum communication. We analyze the security of quantum key distribution as a function of the (partial) knowledge the eavesdropper has about the future choices of measurement settings which are made by the authorized parties (e.g. on the basis of some quasi-random generator). We show that the equivalence between the violation of Bell's inequality and the efficient extraction of a secure key - which exists for the case of complete freedom (no setting knowledge) - is lost unless one adapts the bound of the inequality according to this lack of freedom.Comment: 7 pages, 2 figures, incorporated referee comment

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