25,811 research outputs found
Hamilton-Jacobi Approach for Power-Law Potentials
The classical and relativistic Hamilton-Jacobi approach is applied to the
one-dimensional homogeneous potential, , where and
are continuously varying parameters. In the non-relativistic case, the
exact analytical solution is determined in terms of , and the total
energy . It is also shown that the non-linear equation of motion can be
linearized by constructing a hypergeometric differential equation for the
inverse problem . A variable transformation reducing the general problem
to that one of a particle subjected to a linear force is also established. For
any value of , it leads to a simple harmonic oscillator if , an
"anti-oscillator" if , or a free particle if E=0. However, such a
reduction is not possible in the relativistic case. For a bounded relativistic
motion, the first order correction to the period is determined for any value of
. For , it is found that the correction is just twice that one
deduced for the simple harmonic oscillator (), and does not depend on the
specific value of .Comment: 12 pages, Late
Jeans' gravitational instability and nonextensive kinetic theory
The concept of Jeans gravitational instability is rediscussed in the
framework of nonextensive statistics and its associated kinetic theory. A
simple analytical formula generalizing the Jeans criterion is derived by
assuming that the unperturbed self- gravitating collisionless gas is
kinetically described by the -parameterized class of power law velocity
distributions. It is found that the critical values of wavelength and mass
depend explicitly on the nonextensive -parameter. The standard Jeans
wavelength derived for a Maxwellian distribution is recovered in the limiting
case =1. For power-law distributions with cutoff, the instability condition
is weakened with the system becoming unstable even for wavelengths of the
disturbance smaller than the standard Jeans length .Comment: 5 pages, including 3 figures. Accepted for publication in A&
New coupled quintessence cosmology
A component of dark energy has been recently proposed to explain the current
acceleration of the Universe. Unless some unknown symmetry in Nature prevents
or suppresses it, such a field may interact with the pressureless component of
dark matter, giving rise to the so-called models of coupled quintessence. In
this paper we propose a new cosmological scenario where radiation and baryons
are conserved, while the dark energy component is decaying into cold dark
matter (CDM). The dilution of CDM particles, attenuated with respect to the
usual scaling due to the interacting process, is characterized by a
positive parameter , whereas the dark energy satisfies the equation
of state (). We carry out a joint statistical
analysis involving recent observations from type Ia supernovae, baryon acoustic
oscillation peak, and Cosmic Microwave Background shift parameter to check the
observational viability of the coupled quintessence scenario here proposed.Comment: 7 pages, 7 figures. Minor corrections to match published versio
Is CDM an effective CCDM cosmology?
We show that a cosmology driven by gravitationally induced particle
production of all non-relativistic species existing in the present Universe
mimics exactly the observed flat accelerating CDM cosmology with just
one dynamical free parameter. This kind of scenario includes the creation cold
dark matter (CCDM) model [Lima, Jesus & Oliveira, JCAP 011(2010)027] as a
particular case and also provides a natural reduction of the dark sector since
the vacuum component is not needed to accelerate the Universe. The new cosmic
scenario is equivalent to CDM both at the background and perturbative
levels and the associated creation process is also in agreement with the
universality of the gravitational interaction and equivalence principle.
Implicitly, it also suggests that the present day astronomical observations
cannot be considered the ultimate proof of cosmic vacuum effects in the evolved
Universe because CDM may be only an effective cosmology.Comment: 6 pages, 2 figures, changes in the abstract, introduction, new
references and typo correction
Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model
We investigate the phase diagram of a spin- Ising model on a cubic
lattice, with competing interactions between nearest and next-nearest neighbors
along an axial direction, and fully connected spins on the sites of each
perpendicular layer. The problem is formulated in terms of a set of
noninteracting Ising chains in a position-dependent field. At low temperatures,
as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising
(ANNNI) model, there are many distinct spatially commensurate phases that
spring from a multiphase point of infinitely degenerate ground states. As
temperature increases, we confirm the existence of a branching mechanism
associated with the onset of higher-order commensurate phases. We check that
the ferromagnetic phase undergoes a first-order transition to the modulated
phases. Depending on a parameter of competition, the wave number of the striped
patterns locks in rational values, giving rise to a devil's staircase. We
numerically calculate the Hausdorff dimension associated with these
fractal structures, and show that increases with temperature but seems
to reach a limiting value smaller than .Comment: 17 pages, 6 figure
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