5,696 research outputs found
Peaks in the CMBR power spectrum. I. Mathematical analysis of the associated real space features
The purpose of our study is to understand the mathematical origin in real
space of modulated and damped sinusoidal peaks observed in cosmic microwave
background radiation anisotropies. We use the theory of the Fourier transform
to connect localized features of the two-point correlation function in real
space to oscillations in the power spectrum. We also illustrate analytically
and by means of Monte Carlo simulations the angular correlation function for
distributions of filled disks with fixed or variable radii capable of
generating oscillations in the power spectrum. While the power spectrum shows
repeated information in the form of multiple peaks and oscillations, the
angular correlation function offers a more compact presentation that condenses
all the information of the multiple peaks into a localized real space feature.
We have seen that oscillations in the power spectrum arise when there is a
discontinuity in a given derivative of the angular correlation function at a
given angular distance. These kinds of discontinuities do not need to be abrupt
in an infinitesimal range of angular distances but may also be smooth, and can
be generated by simply distributing excesses of antenna temperature in filled
disks of fixed or variable radii on the sky, provided that there is a non-null
minimum radius and/or the maximum radius is constrained.Comment: accepted to be published in Physica
Implications of effective axial-vector coupling of gluon for spin polarizations at the LHC
We analyze the impact of effective axial-vector coupling of the gluon on spin
polarization observables in pair production at the LHC. Working at
leading order in QCD, we compute the spin-correlation and left-right
spin asymmetry coefficients in the helicity basis in the laboratory frame as
functions of the new physics scale associated with this coupling. We
found that the invariant mass dependent asymmetries are more
sensitive to the scale than the corresponding inclusive ones, in
particular when suitable cuts selecting high invariant mass regions
are imposed. In the context of this scenario, we show that the LHC has
potential either to confirm or to rule out the Tevatron FB top asymmetry
anomaly by analyzing the spin-correlation and left-right
polarization asymmetries. On the other hand, stringent lower bound on the new
physics scale can be set in this scenario if no significant
deviations from the SM predictions for those observables will be measured.Comment: 26 pages, 8 figures, same as published version in PRD. Few
modifications in the text and one new reference adde
A perturbative approach to the Bak-Sneppen Model
We study the Bak-Sneppen model in the probabilistic framework of the Run Time
Statistics (RTS). This model has attracted a large interest for its simplicity
being a prototype for the whole class of models showing Self-Organized
Criticality. The dynamics is characterized by a self-organization of almost all
the species fitnesses above a non-trivial threshold value, and by a lack of
spatial and temporal characteristic scales. This results in {\em avalanches} of
activity power law distributed. In this letter we use the RTS approach to
compute the value of , the value of the avalanche exponent and the
asymptotic distribution of minimal fitnesses.Comment: 4 pages, 3 figures, to be published on Physical Review Letter
1-d gravity in infinite point distributions
The dynamics of infinite, asymptotically uniform, distributions of
self-gravitating particles in one spatial dimension provides a simple toy model
for the analogous three dimensional problem. We focus here on a limitation of
such models as treated so far in the literature: the force, as it has been
specified, is well defined in infinite point distributions only if there is a
centre of symmetry (i.e. the definition requires explicitly the breaking of
statistical translational invariance). The problem arises because naive
background subtraction (due to expansion, or by "Jeans' swindle" for the static
case), applied as in three dimensions, leaves an unregulated contribution to
the force due to surface mass fluctuations. Following a discussion by
Kiessling, we show that the problem may be resolved by defining the force in
infinite point distributions as the limit of an exponentially screened pair
interaction. We show that this prescription gives a well defined (finite) force
acting on particles in a class of perturbed infinite lattices, which are the
point processes relevant to cosmological N-body simulations. For identical
particles the dynamics of the simplest toy model is equivalent to that of an
infinite set of points with inverted harmonic oscillator potentials which
bounce elastically when they collide. We discuss previous results in the
literature, and present new results for the specific case of this simplest
(static) model starting from "shuffled lattice" initial conditions. These show
qualitative properties (notably its "self-similarity") of the evolution very
similar to those in the analogous simulations in three dimensions, which in
turn resemble those in the expanding universe.Comment: 20 pages, 8 figures, small changes (section II shortened, added
discussion in section IV), matches final version to appear in PR
Non perturbative renormalization group approach to surface growth
We present a recently introduced real space renormalization group (RG)
approach to the study of surface growth.
The method permits us to obtain the properties of the KPZ strong coupling
fixed point, which is not accessible to standard perturbative field theory
approaches. Using this method, and with the aid of small Monte Carlo
calculations for systems of linear size 2 and 4, we calculate the roughness
exponent in dimensions up to d=8. The results agree with the known numerical
values with good accuracy. Furthermore, the method permits us to predict the
absence of an upper critical dimension for KPZ contrarily to recent claims. The
RG scheme is applied to other growth models in different universality classes
and reproduces very well all the observed phenomenology and numerical results.
Intended as a sort of finite size scaling method, the new scheme may simplify
in some cases from a computational point of view the calculation of scaling
exponents of growth processes.Comment: Invited talk presented at the CCP1998 (Granada
Initial conditions, Discreteness and non-linear structure formation in cosmology
In this lecture we address three different but related aspects of the initial
continuous fluctuation field in standard cosmological models. Firstly we
discuss the properties of the so-called Harrison-Zeldovich like spectra. This
power spectrum is a fundamental feature of all current standard cosmological
models. In a simple classification of all stationary stochastic processes into
three categories, we highlight with the name ``super-homogeneous'' the
properties of the class to which models like this, with , belong. In
statistical physics language they are well described as glass-like. Secondly,
the initial continuous density field with such small amplitude correlated
Gaussian fluctuations must be discretised in order to set up the initial
particle distribution used in gravitational N-body simulations. We discuss the
main issues related to the effects of discretisation, particularly concerning
the effect of particle induced fluctuations on the statistical properties of
the initial conditions and on the dynamical evolution of gravitational
clustering.Comment: 28 pages, 1 figure, to appear in Proceedings of 9th Course on
Astrofundamental Physics, International School D. Chalonge, Kluwer, eds N.G.
Sanchez and Y.M. Pariiski, uses crckapb.st pages, 3 figure, ro appear in
Proceedings of 9th Course on Astrofundamental Physics, International School
D. Chalonge, Kluwer, Eds. N.G. Sanchez and Y.M. Pariiski, uses crckapb.st
Invasion Percolation with Temperature and the Nature of SOC in Real Systems
We show that the introduction of thermal noise in Invasion Percolation (IP)
brings the system outside the critical point. This result suggests a possible
definition of SOC systems as ordinary critical systems where the critical point
correspond to set to 0 one of the parameters. We recover both IP and EDEN
model, for , and respectively. For small we find a
dynamical second order transition with correlation length diverging when .Comment: 4 pages, 2 figure
A dynamical classification of the range of pair interactions
We formalize a classification of pair interactions based on the convergence
properties of the {\it forces} acting on particles as a function of system
size. We do so by considering the behavior of the probability distribution
function (PDF) P(F) of the force field F in a particle distribution in the
limit that the size of the system is taken to infinity at constant particle
density, i.e., in the "usual" thermodynamic limit. For a pair interaction
potential V(r) with V(r) \rightarrow \infty) \sim 1/r^a defining a {\it
bounded} pair force, we show that P(F) converges continuously to a well-defined
and rapidly decreasing PDF if and only if the {\it pair force} is absolutely
integrable, i.e., for a > d-1, where d is the spatial dimension. We refer to
this case as {\it dynamically short-range}, because the dominant contribution
to the force on a typical particle in this limit arises from particles in a
finite neighborhood around it. For the {\it dynamically long-range} case, i.e.,
a \leq d-1, on the other hand, the dominant contribution to the force comes
from the mean field due to the bulk, which becomes undefined in this limit. We
discuss also how, for a \leq d-1 (and notably, for the case of gravity, a=d-2)
P(F) may, in some cases, be defined in a weaker sense. This involves a
regularization of the force summation which is generalization of the procedure
employed to define gravitational forces in an infinite static homogeneous
universe. We explain that the relevant classification in this context is,
however, that which divides pair forces with a > d-2 (or a < d-2), for which
the PDF of the {\it difference in forces} is defined (or not defined) in the
infinite system limit, without any regularization. In the former case dynamics
can, as for the (marginal) case of gravity, be defined consistently in an
infinite uniform system.Comment: 12 pages, 1 figure; significantly shortened and focussed, additional
references, version to appear in J. Stat. Phy
Force distribution in a randomly perturbed lattice of identical particles with pair interaction
We study the statistics of the force felt by a particle in the class of
spatially correlated distribution of identical point-like particles,
interacting via a pair force (i.e. gravitational or Coulomb), and
obtained by randomly perturbing an infinite perfect lattice. In the first part
we specify the conditions under which the force on a particle is a well defined
stochastic quantity. We then study the small displacements approximation,
giving both the limitations of its validity, and, when it is valid, an
expression for the force variance. In the second part of the paper we extend to
this class of particle distributions the method introduced by Chandrasekhar to
study the force probability density function in the homogeneous Poisson
particle distribution. In this way we can derive an approximate expression for
the probability distribution of the force over the full range of perturbations
of the lattice, i.e., from very small (compared to the lattice spacing) to very
large where the Poisson limit is recovered. We show in particular the
qualitative change in the large-force tail of the force distribution between
these two limits. Excellent accuracy of our analytic results is found on
detailed comparison with results from numerical simulations. These results
provide basic statistical information about the fluctuations of the
interactions (i) of the masses in self-gravitating systems like those
encountered in the context of cosmological N-body simulations, and (ii) of the
charges in the ordered phase of the One Component Plasma.Comment: 23 pages, 10 figure
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