4,290 research outputs found

    Continuous slice functional calculus in quaternionic Hilbert spaces

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    The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic C∗C^*--algebras and to define, on each of these C∗C^*--algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.Comment: 71 pages, some references added. Accepted for publication in Reviews in Mathematical Physic

    On dynamical r-matrices obtained from Dirac reduction and their generalizations to affine Lie algebras

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    According to Etingof and Varchenko, the classical dynamical Yang-Baxter equation is a guarantee for the consistency of the Poisson bracket on certain Poisson-Lie groupoids. Here it is noticed that Dirac reductions of these Poisson manifolds give rise to a mapping from dynamical r-matrices on a pair \L\subset \A to those on another pair \K\subset \A, where \K\subset \L\subset \A is a chain of Lie algebras for which \L admits a reductive decomposition as \L=\K+\M. Several known dynamical r-matrices appear naturally in this setting, and its application provides new r-matrices, too. In particular, we exhibit a family of r-matrices for which the dynamical variable lies in the grade zero subalgebra of an extended affine Lie algebra obtained from a twisted loop algebra based on an arbitrary finite dimensional self-dual Lie algebra.Comment: 19 pages, LaTeX, added a reference and a footnote and removed some typo

    Direct Observation of Hyperfine Quenching of the (2)3p0 Level in Helium-Like Nickel

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    Journals published by the American Physical Society can be found at http://publish.aps.org/We report a clear demonstration of the effect of hyperfine quenching of a forbidden transition by direct comparison of the lifetimes of the 2 3P0 level in the heliumlike isotopes Ni-61(26+) and Ni-58(26+). We find the quenched lifetime of the 2 3P0 level in Ni-61(26+) to be 470(50) ps. From this we deduce the 2 3P0-2 3P1 energy splitting to be 2.33(15) eV. We also report a measurement of the lifetime of the 2 3P2 level in Ni-58(26+), which is found to be 70(3) ps

    A comparison of the healthiness of packaged foods and beverages from 12 countries using the Health Star Rating nutrient profiling system, 2013-2018

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    We compared the healthiness of packaged foods and beverages between selected countries using the Health Star Rating (HSR) nutrient profiling system. Packaged food and beverage data collected 2013-2018 were obtained for Australia, Canada, Chile, China, India, Hong Kong, Mexico, New Zealand, Slovenia, South Africa, the UK, and USA. Each product was assigned to a food or beverage category and mean HSR was calculated overall by category and by country. Median energy density (kJ/100 g), saturated fat (g/100 g), total sugars (g/100 g) and sodium (mg/100 g) contents were calculated. Countries were ranked by mean HSR and median nutrient levels. Mean HSR for all products (n = 394,815) was 2.73 (SD 1.38) out of 5.0 (healthiest profile). The UK, USA, Australia and Canada ranked highest for overall nutrient profile (HSR 2.74-2.83) and India, Hong Kong, China and Chile ranked lowest (HSR 2.27-2.44). Countries with higher overall HSR generally ranked better with respect to nutrient levels. India ranked consistently in the least healthy third for all measures. There is considerable variability in the healthiness of packaged foods and beverages in different countries. The finding that packaged foods and beverages are less healthy in middle-income countries such as China and India suggests that nutrient profiling is an important tool to enable policymakers and industry actors to reformulate products available in the marketplace to reduce the risk of obesity and NCDs among populations

    Rigorous investigation of the reduced density matrix for the ideal Bose gas in harmonic traps by a loop-gas-like approach

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    In this paper, we rigorously investigate the reduced density matrix (RDM) associated to the ideal Bose gas in harmonic traps. We present a method based on a sum-decomposition of the RDM allowing to treat not only the isotropic trap, but also general anisotropic traps. When focusing on the isotropic trap, the method is analogous to the loop-gas approach developed by W.J. Mullin in [38]. Turning to the case of anisotropic traps, we examine the RDM for some anisotropic trap models corresponding to some quasi-1D and quasi-2D regimes. For such models, we bring out an additional contribution in the local density of particles which arises from the mesoscopic loops. The close connection with the occurrence of generalized-BEC is discussed. Our loop-gas-like approach provides relevant information which can help guide numerical investigations on highly anisotropic systems based on the Path Integral Monte Carlo (PIMC) method.Comment: v3: Minor modifications of v2. v2: Major modifications: the former version (v1) has been completely rewritten. New results concerning the anisotropic traps and generalized Bose-Einstein condensation have been added. The connection with the loop-gas approach is further discussed. 40 page

    Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

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    `Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a lattice. Related ideas appeared in recent publications and we show that the examples treated there are special cases of umbral calculus. This observation then suggests various generalizations of these examples. A special umbral representation of the canonical commutation relations given in terms of the position and momentum operator on a lattice is investigated in detail.Comment: 19 pages, Late
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