25,071 research outputs found
Eigenvalue spectrum for single particle in a spheroidal cavity: A Semiclassical approach
Following the semiclassical formalism of Strutinsky et al., we have obtained
the complete eigenvalue spectrum for a particle enclosed in an infinitely high
spheroidal cavity. Our spheroidal trace formula also reproduces the results of
a spherical billiard in the limit . Inclusion of repetition of each
family of the orbits with reference to the largest one significantly improves
the eigenvalues of sphere and an exact comparison with the quantum mechanical
results is observed upto the second decimal place for . The
contributions of the equatorial, the planar (in the axis of symmetry plane) and
the non-planar(3-Dimensional) orbits are obtained from the same trace formula
by using the appropriate conditions. The resulting eigenvalues compare very
well with the quantum mechanical eigenvalues at normal deformation. It is
interesting that the partial sum of equatorial orbits leads to eigenvalues with
maximum angular momentum projection, while the summing of planar orbits leads
to eigenvalues with except for L=1. The remaining quantum mechanical
eigenvalues are observed to arise from the 3-dimensional(3D) orbits. Very few
spurious eigenvalues arise in these partial sums. This result establishes the
important role of 3D orbits even at normal deformations.Comment: 17 pages, 7 ps figure
A flat space-time model of the Universe
We propose a model of the Universe based on Minkowski flat space-time metric.
In this model the space-time does not evolve. Instead the matter evolves such
that all the mass parameters increase with time. We construct a model based on
unimodular gravity to show how this can be accomplished within the framework of
flat space-time. We show that the model predicts the Hubble law if the masses
increase with time. Furthermore we show that it fits the high z supernova data
in a manner almost identical to the standard Big Bang model. Furthermore we
show that at early times the Universe is dominated by radiative energy density.
The phenomenon of recombination also arises in our model and hence predicts the
existence of CMBR. However a major difference with the standard Big Bang is
that the radiative temperature and energy density does not evolve in our model.
Furthermore we argue that the basic motivation for inflation is absent in our
model.Comment: 11 pages, no figures, changes in presentatio
Extreme value distributions for weakly correlated fitnesses in block model
We study the limit distribution of the largest fitness for two models of
weakly correlated and identically distributed random fitnesses. The correlated
fitness is given by a linear combination of a fixed number of independent
random variables drawn from a common parent distribution. We find that for
certain class of parent distributions, the extreme value distribution for
correlated random variables can be related either to one of the known limit
laws for independent variables or the parent distribution itself. For other
cases, new limiting distributions appear. The conditions under which these
results hold are identified.Comment: Expanded, added reference
Adaptation dynamics of the quasispecies model
We study the adaptation dynamics of an initially maladapted population
evolving via the elementary processes of mutation and selection. The evolution
occurs on rugged fitness landscapes which are defined on the multi-dimensional
genotypic space and have many local peaks separated by low fitness valleys. We
mainly focus on the Eigen's model that describes the deterministic dynamics of
an infinite number of self-replicating molecules. In the stationary state, for
small mutation rates such a population forms a {\it quasispecies} which
consists of the fittest genotype and its closely related mutants. The
quasispecies dynamics on rugged fitness landscape follow a punctuated (or
step-like) pattern in which a population jumps from a low fitness peak to a
higher one, stays there for a considerable time before shifting the peak again
and eventually reaches the global maximum of the fitness landscape. We
calculate exactly several properties of this dynamical process within a
simplified version of the quasispecies model.Comment: Proceedings of Statphys conference at IIT Guwahati, to be published
in Praman
Gravitational lensing constraint on the cosmic equation of state
Recent redshift-distance measurements of Type Ia supernovae (SNe Ia) at
cosmological distances suggest that two-third of the energy density of the
universe is dominated by dark energy component with an effective negative
pressure. This dark energy component is described by the equation of state
. We use gravitational lensing statistics to
constrain the equation of state of this dark energy. We use ,
image separation distribution function of lensed quasars, as a tool to probe
. We find that for the observed range of ,
should lie between in order to have five lensed quasars
in a sample of 867 optical quasars. This limit is highly sensitive to lens and
Schechter parameters and evolution of galaxies.Comment: Modified results and inclusion of calculations with new set of
parameter
An interacting model for the cosmological dark sector
We discuss a new interacting model for the cosmological dark sector in which
the attenuated dilution of cold dark matter scales as , where f(a)
is an arbitrary function of the cosmic scale factor . From thermodynamic
arguments, we show that f(a) is proportional to entropy source of the particle
creation process. In order to investigate the cosmological consequences of this
kind of interacting models, we expand f(a) in a power series and viable
cosmological solutions are obtained. Finally, we use current observational data
to place constraints on the interacting function f(a).Comment: 5 pages, 3 figures, Phys. Rev. D (in press
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