326,206 research outputs found
Geometric Formulation for Partially Massless Fields
The manifestly gauge invariant formulation for free symmetric partially
massless fields in is given in terms of gauge connections and
linearized curvatures that take values in the irreducible representations of
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
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
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
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
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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