3,863 research outputs found
Influence of Super-Horizon Scales on Cosmological Observables Generated during Inflation
Using the techniques of out-of-equilibrium field theory, we study the
influence on the properties of cosmological perturbations generated during
inflation on observable scales coming from fluctuations corresponding today to
scales much bigger than the present Hubble radius. We write the effective
action for the coarse-grained inflaton perturbations integrating out the
sub-horizon modes, which manifest themselves as a colored noise and lead to
memory effects. Using the simple model of a scalar field with cubic
self-interactions evolving in a fixed de Sitter background, we evaluate the
two- and three-point correlation function on observable scales. Our basic
procedure shows that perturbations do preserve some memory of the
super-horizon-scale dynamics, in the form of scale-dependent imprints in the
statistical moments. In particular, we find a blue tilt of the power-spectrum
on large scales, in agreement with the recent results of the WMAP collaboration
which show a suppression of the lower multipoles in the Cosmic Microwave
Background anisotropies, and a substantial enhancement of the intrinsic
non-Gaussianity on large scalesComment: 19 pages, 5 figures. One reference adde
Thierry Aubry «Des Gravures en plein air d'au moins 15 000 ans»
info:eu-repo/semantics/publishedVersio
Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions
A general procedure to get the explicit solution of the equations of motion
for N-body classical Hamiltonian systems equipped with coalgebra symmetry is
introduced by defining a set of appropriate collective variables which are
based on the iterations of the coproduct map on the generators of the algebra.
In this way several examples of N-body dynamical systems obtained from
q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2)
Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of
Ruijsenaars type arising from the same (non co-boundary) q-deformation of the
(1+1) Poincare' algebra. Also, a unified interpretation of all these systems as
different Poisson-Lie dynamics on the same three dimensional solvable Lie group
is given.Comment: 19 Latex pages, No figure
Hamiltonian flows on null curves
The local motion of a null curve in Minkowski 3-space induces an evolution
equation for its Lorentz invariant curvature. Special motions are constructed
whose induced evolution equations are the members of the KdV hierarchy. The
null curves which move under the KdV flow without changing shape are proven to
be the trajectories of a certain particle model on null curves described by a
Lagrangian linear in the curvature. In addition, it is shown that the curvature
of a null curve which evolves by similarities can be computed in terms of the
solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio
Binary trees, coproducts, and integrable systems
We provide a unified framework for the treatment of special integrable
systems which we propose to call "generalized mean field systems". Thereby
previous results on integrable classical and quantum systems are generalized.
Following Ballesteros and Ragnisco, the framework consists of a unital algebra
with brackets, a Casimir element, and a coproduct which can be lifted to higher
tensor products. The coupling scheme of the iterated tensor product is encoded
in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new
appendices adde
A holographic perspective on phonons and pseudo-phonons
We analyze the concomitant spontaneous breaking of translation and conformal
symmetries by introducing in a CFT a complex scalar operator that acquires a
spatially dependent expectation value. The model, inspired by the holographic
Q-lattice, provides a privileged setup to study the emergence of phonons from a
spontaneous translational symmetry breaking in a conformal field theory and
offers valuable hints for the treatment of phonons in QFT at large. We first
analyze the Ward identity structure by means of standard QFT techniques,
considering both spontaneous and explicit symmetry breaking. Next, by
implementing holographic renormalization, we show that the same set of Ward
identities holds in the holographic Q-lattice. Eventually, relying on the
holographic and QFT results, we study the correlators realizing the symmetry
breaking pattern and how they encode information about the low-energy spectrum.Comment: 31+1 pages, version accepted on JHE
Closed trajectories of a particle model on null curves in anti-de Sitter 3-space
We study the existence of closed trajectories of a particle model on null
curves in anti-de Sitter 3-space defined by a functional which is linear in the
curvature of the particle path. Explicit expressions for the trajectories are
found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur
An evolutionary model with Turing machines
The development of a large non-coding fraction in eukaryotic DNA and the
phenomenon of the code-bloat in the field of evolutionary computations show a
striking similarity. This seems to suggest that (in the presence of mechanisms
of code growth) the evolution of a complex code can't be attained without
maintaining a large inactive fraction. To test this hypothesis we performed
computer simulations of an evolutionary toy model for Turing machines, studying
the relations among fitness and coding/non-coding ratio while varying mutation
and code growth rates. The results suggest that, in our model, having a large
reservoir of non-coding states constitutes a great (long term) evolutionary
advantage.Comment: 16 pages, 7 figure
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