326,206 research outputs found

    Geometric Formulation for Partially Massless Fields

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    The manifestly gauge invariant formulation for free symmetric partially massless fields in (A)dSd(A)dS_d is given in terms of gauge connections and linearized curvatures that take values in the irreducible representations of (o(d1,2))o(d,1)(o(d-1,2)) o(d,1) described by two-row Young tableaux, in which the lengths of the first and second row are, respectively, associated with spin and depth of partial masslessness.Comment: LaTeX, 42 pages. Published in Nucl. Phys.

    Adsorption of symmetric random copolymer onto symmetric random surface: the annealed case

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    Adsorption of a symmetric (AB) random copolymer (RC) onto a symmetric (ab) random heterogeneous surface (RS) is studied in the annealed approximation by using a two-dimensional partially directed walk model of the polymer. We show that in the symmetric case, the expected a posteriori compositions of the RC and the RS have correct values (corresponding to their a priori probabilities) and do not change with the temperature, whereas second moments of monomers and sites distributions in the RC and RS change. This indicates that monomers and sites do not interconvert but only rearrange in order to provide better matching between them and, as a result, a stronger adsorption of the RC on the RS. However, any violation of the system symmetry shifts equilibrium towards the major component and/or more favorable contacts and leads to interconversion of monomers and sites.Comment: 15 pages, 7 figure

    On the dynamics of Extrasolar Planetary Systems under dissipation. Migration of planets

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    We study the dynamics of planetary systems with two planets moving in the same plane, when frictional forces act on the two planets, in addition to the gravitational forces. The model of the general three-body problem is used. Different laws of friction are considered. The topology of the phase space is essential in understanding the evolution of the system. The topology is determined by the families of stable and unstable periodic orbits, both symmetric and non symmetric. It is along the stable families, or close to them, that the planets migrate when dissipative forces act. At the critical points where the stability along the family changes, there is a bifurcation of a new family of stable periodic orbits and the migration process changes route and follows the new stable family up to large eccentricities or to a chaotic region. We consider both resonant and non resonant planetary systems. The 2/1, 3/1 and 3/2 resonances are studied. The migration to larger or smaller eccentricities depends on the particular law of friction. Also, in some cases the semimajor axes increase and in other cases they are stabilized. For particular laws of friction and for special values of the parameters of the frictional forces, it is possible to have partially stationary solutions, where the eccentricities and the semimajor axes are fixed.Comment: Accepted in Celestial Mechanics and Dynamical Astronom

    Additive monotones for resource theories of parallel-combinable processes with discarding

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    A partitioned process theory, as defined by Coecke, Fritz, and Spekkens, is a symmetric monoidal category together with an all-object-including symmetric monoidal subcategory. We think of the morphisms of this category as processes, and the morphisms of the subcategory as those processes that are freely executable. Via a construction we refer to as parallel-combinable processes with discarding, we obtain from this data a partially ordered monoid on the set of processes, with f > g if one can use the free processes to construct g from f. The structure of this partial order can then be probed using additive monotones: order-preserving monoid homomorphisms with values in the real numbers under addition. We first characterise these additive monotones in terms of the corresponding partitioned process theory. Given enough monotones, we might hope to be able to reconstruct the order on the monoid. If so, we say that we have a complete family of monotones. In general, however, when we require our monotones to be additive monotones, such families do not exist or are hard to compute. We show the existence of complete families of additive monotones for various partitioned process theories based on the category of finite sets, in order to shed light on the way such families can be constructed.Comment: In Proceedings QPL 2015, arXiv:1511.0118

    Discriminants in the Grothendieck Ring

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    We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singularities. We focus on the space of partially labeled points on a variety X, and linear systems on X. These are connected --- we use the first to understand the second. We describe their classes in the Grothendieck ring of varieties, as the number of points gets large, or as the line bundle gets very positive. They stabilize in an appropriate sense, and their stabilization is given in terms of motivic zeta values. Motivated by our results, we conjecture that the symmetric powers of geometrically irreducible varieties stabilize in the Grothendieck ring (in an appropriate sense). Our results extend parallel results in both arithmetic and topology. We give a number of reasons for considering these questions, and propose a number of new conjectures, both arithmetic and topological.Comment: 39 pages, updated with progress by others on various conjecture
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