Dual Killing-Yano symmetry and multipole moments in electromagnetism and mechanics of continua

In this work we introduce the Killing-Yano symmetry on the phase space and we investigate the symplectic structure on the space of Killing-Yano tensors. We perform the detailed analyze of the $n$-dimensional flat space and the Riemaniann manifolds with constant scalar curvature. We investigate the form of some multipole tensors, which arise in the expansion of a system of charges and currents, in terms of second-order Killing-Yano tensors in the phase space of classical mechanics. We find some relations between these tensors and the generators of dynamical symmetries like the angular momentum, the mass-inertia tensor, the conformal operator and the momentum conjugate Runge-Lenz vector.Comment: 11 pages LaTeX, no figures, content enlarged and revised, accepted for publication in Helvetica Physica Act

Testing the Cactus code on exact solutions of the Einstein field equations

The article presents a series of numerical simulations of exact solutions of the Einstein equations performed using the Cactus code, a complete 3-dimensional machinery for numerical relativity. We describe an application (``thorn'') for the Cactus code that can be used for evolving a variety of exact solutions, with and without matter, including solutions used in modern cosmology for modeling the early stages of the universe. Our main purpose has been to test the Cactus code on these well-known examples, focusing mainly on the stability and convergence of the code.Comment: 18 pages, 18 figures, Late

Higher derivatives and brane-localised kinetic terms in gauge theories on orbifolds

We perform a detailed analysis of one-loop corrections to the self-energy of the (off-shell) gauge bosons in six-dimensional N=1 supersymmetric gauge theories on orbifolds. After discussing the Abelian case in the standard Feynman diagram approach, we extend the analysis to the non-Abelian case by employing the method of an orbifold-compatible one-loop effective action for a classical background gauge field. We find that bulk higher derivative and brane-localised gauge kinetic terms are required to cancel one-loop divergences of the gauge boson self energy. After their renormalisation we study the momentum dependence of both the higher derivative coupling h(k^2) and the {\it effective} gauge coupling g_eff(k^2). For momenta smaller than the compactification scales, we obtain the 4D logarithmic running of g_eff(k^2), with suppressed power-like corrections, while the higher derivative coupling is constant. We present in detail the threshold corrections to the low energy gauge coupling, due to the massive bulk modes. At momentum scales above the compactification scales, the higher derivative operator becomes important and leads to a power-like running of g_eff(k^2) with respect to the momentum scale. The coefficient of this running is at all scales equal to the renormalised coupling of the higher derivative operator which ensures the quantum consistency of the model. We discuss the relation to the similar one-loop correction in the heterotic string, to show that the higher derivative operators are relevant in that case too, since the field theory limit of the one-loop string correction does not commute with the infrared regularisation of the (on-shell) string result.Comment: 1+45 pages, 2 figures, JHEP style file, version to be published in JHE

On the Observation of Phase Transitions in Collisions of Elementary Matter

We investigate the excitation function of directed flow, which can provide a clear signature of the creation of the QGP and demonstrate that the minimum of the directed flow does not correspond to the softest point of the EoS for isentropic expansion. A novel technique measuring the compactness is introduced to determine the QGP transition in relativistic-heavy ion collisions: The QGP transition will lead to higher compression and therefore to higher compactness of the source in coordinate space. This effect can be observed by pion interferometry. We propose to measure the compactness of the source in the appropriate principal axis frame of the compactness tensor in coordinate space.Comment: LaTeX, 8 pages, 6 figures, Conference proceedings to CRIS 2000, 3rd Catania Relativistic Ion Studie

Direct Emission of multiple strange baryons in ultrarelativistic heavy-ion collisions from the phase boundary

We discuss a model for the space-time evolution of ultrarelativistic heavy-ion collisions which employs relativistic hydrodynamics within one region of the forward light-cone, and microscopic transport theory (i.e. UrQMD) in the complement. Our initial condition consists of a quark-gluon plasma which expands hydrodynamically and hadronizes. After hadronization the solution eventually changes from expansion in local equilibrium to free streaming, as determined selfconsistently by the interaction rates between the hadrons and the local expansion rate. We show that in such a scenario the inverse slopes of the $m_T$-spectra of multiple strange baryons ($\Xi$, $\Omega$) are practically unaffected by the purely hadronic stage of the reaction, while the flow of $p$'s and $\Lambda$'s increases. Moreover, we find that the rather ``soft'' transverse expansion at RHIC energies (due to a first-order phase transition) is not washed out by strong rescattering in the hadronic stage. The earlier kinetic freeze-out as compared to SPS-energies results in similar inverse slopes (of the $m_T$-spectra of the hadrons in the final state) at RHIC and SPS energies.Comment: 4 pages, 3 figures, statistics for Omegas improved, slight revision of the manuscript (expansion of hadronization volume more emphasized, pi-Omega scattering is discussed very briefly

Nuclear collective dynamics within Vlasov approach

We discuss, in an investigation based on Vlasov equation, the properties of the isovector modes in nuclear matter and atomic nuclei in relation with the symmetry energy. We obtain numerically the dipole response and determine the strength function for various systems, including a chain of Sn isotopes. We consider for the symmetry energy three parametrizations with density providing similar values at saturation but which manifest very different slopes around this point. In this way we can explore how the slope affects the collective response of finite nuclear systems. We focus first on the dipole polarizability and show that while the model is able to describe the expected mass dependence, A^{5/3}, it also demonstrates that this quantity is sensitive to the slope parameter of the symmetry energy. Then, by considering the Sn isotopic chain, we investigate the emergence of a collective mode, the Pygmy Dipole Resonance (PDR), when the number of neutrons in excess increases. We show that the total energy-weighted sum rule exhausted by this mode has a linear dependence with the square of isospin I=(N-Z)/A, again sensitive to the slope of the symmetry energy with density. Therefore the polarization effects in the isovector density have to play an important role in the dynamics of PDR. These results provide additional hints in the investigations aiming to extract the properties of symmetry energy below saturation.Comment: 7 pages, 6 figure