80,377 research outputs found

    Factorization of weakly continuous holomorphic mappings

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    We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly {\it uniformly\/} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Herv\'es and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser one. However, we show that it need not be true for a stronger topology, thus answering a question raised by Aron. As an application of the first result, we prove that a holomorphic mapping ff between complex Banach spaces is weakly uniformly continuous on bounded subsets if and only if it admits a factorization of the form f=gSf=g\circ S, where SS is a compact operator and gg a holomorphic mapping

    Dynamical evolution of the chiral magnetic effect: Applications to the quark-gluon plasma

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    We study the dynamical evolution of the so-called chiral magnetic effect in an electromagnetic conductor. To this end, we consider the coupled set of corresponding Maxwell and chiral anomaly equations, and we prove that these can be derived from chiral kinetic theory. After integrating the chiral anomaly equation over space in a closed volume, it leads to a quantum conservation law of the total helicity of the system. A change in the magnetic helicity density comes together with a modification of the chiral fermion density. We study in Fourier space the coupled set of anomalous equations and we obtain the dynamical evolution of the magnetic fields, magnetic helicity density, and chiral fermion imbalance. Depending on the initial conditions we observe how the helicity might be transferred from the fermions to the magnetic fields, or vice versa, and find that the rate of this transfer also depends on the scale of wavelengths of the gauge fields in consideration. We then focus our attention on the quark-gluon plasma phase, and analyze the dynamical evolution of the chiral magnetic effect in a very simple toy model. We conclude that an existing chiral fermion imbalance in peripheral heavy ion collisions would affect the magnetic field dynamics, and consequently, the charge dependent correlations measured in these experiments.Comment: 41 pages, 14 figures, 3 appendices. Version 2: new global structure (appendix added), more explanations and additional references. Version accepted for publication in Physical Review D journa

    Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory

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    We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function.Comment: 9 pages, no figures. v2: Some comments and more details added, typos fixed and reference list updated. Final version matching the published articl

    A Quantum Quasi-Harmonic Nonlinear Oscillator with an Isotonic Term

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    The properties of a nonlinear oscillator with an additional term kg/x2k_g/x^2, characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, κ\kappa and kgk_g, in such a way that for κ=0\kappa=0 all the characteristics of of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form m(x)=1/(1κx2)m(x)=1/(1 - {\kappa} x^2), with a κ\kappa-dependent non-polynomial rational potential and with an additional isotonic term. The Schr\"odinger equation is exactly solved and the (κ,kg)(\kappa,k_g)-dependent wave functions and bound state energies are explicitly obtained for both κ0\kappa0.Comment: two figure

    New Methodological Approaches for Change in Traditional Sectors: The Case of the Portuguese Fisheries Socio-Economic System

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    This paper summarises the methodological approach and main results of the MARHE project (Employment and Human Resources in the Fisheries Socio-Economic System). This project had as its main aim the search for alternative futures for the fisheries sector in Portugal, with particular attention being paid to the human resources situation and the working and living conditions of the fisheries-dependent populations in the coastal areas. This is a particularly interesting case, since fisheries were once an important activity and they are now in deep recession, even though it is generally recognised that the future utilisation of maritime resources offer an immense potential. As part of the research, a Delphi exercise was implemented involving in two successive stages some of the leading actors and experts dealing with the sector in Portugal. Other initiatives were held in the context of the MARHE project providing direct and indirect inputs to the scenarios and recommendations that were put forward in the sequence of the Delphi exercise. Overall the activities described in the paper contributed to the mobilisation of major actors and to discussions that may have practical implication for the future of the sector, if certain conditions are now met in the follow up to the project.Fisheries; Portugal; human resources; scenarios; labour market
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