119 research outputs found
Constraints on the equation of state from the stability condition of neutron stars
The stellar equilibrium and collapse, including mainly white dwarfs, neutron
stars and supper massive stars, is an interplay between general relativistic
effects and the equation of state of nuclear matter. In the present work, we
use the Chandrasekhar criterion of stellar instability by employing a large
number of realistic equations of state (EoS) of neutron star matter. We mainly
focus on the critical point of transition from stable to unstable
configuration. This point corresponds to the maximum neutron star mass
configuration. We calculate, in each case, the resulting compactness parameter,
, and the corresponding effective adiabatic index, . The role of the trial function is presented and discussed in
details. We found that it holds a model-independent relation between
and . This statement is strongly supported by the
large number of EoS and it is also corroborated by using analytical solutions
of the Einstein's field equations. In addition, we present and discuss the
relation between the maximum rotation rate and the adiabatic index close to the
instability limit. Accurate observational measurements of the upper bound of
the neutron star mass and the corresponding radius, in connection with the
present predictions, may help to impose constraints on the high density part of
the neutron star equation of state.Comment: 15 pages, 1 table, 12 figure
The dependence of information entropy of uniform Fermi systems on correlations and thermal effects
The influence of correlations of uniform Fermi systems (nuclear matter,
electron gas and liquid He) on Shannon's information entropy, , is
studied. is the sum of the information entropies in position and momentum
spaces. It is found that, for three different Fermi systems with different
particle interactions, the correlated part of () depends on the
correlation parameter of the systems or on the discontinuity gap of the
momentum distribution through two parameter expressions. The values of the
parameters characterize the strength of the correlations. A two parameter
expression also holds between and the mean kinetic energy () of
the Fermi system. The study of thermal effects on the uncorrelated electron gas
leads to a relation between the thermal part of () and the
fundamental quantities of temperature, thermodynamical entropy and the mean
kinetic energy. It is found that, in the case of low temperature limit, the
expression connecting with is the same to the one which
connects with . There are only some small differences on the
values of the parameters. Thus, regardless of the reason (correlations or
thermal) that changes , takes almost the same value.Comment: 18 pages, 7 figure
Natural orbitals representation and Fermi sea depletion in finite nuclei and nuclear matter
The natural orbitals and natural occupation numbers of various N = Z, sp and
sd shell nuclei are calculated by applying a correlated one-body density
matrix. The correlated density matrix has been evaluated by considering central
correlations of Jastrow type and an approximation named factor cluster
expansion. The correlation effects on the natural orbitals, natural occupation
numbers and the Fermi sea depletion are discussed and analysed. In addition, an
approximate expression for the correlated one-body density matrix of the
nuclear matter has been used for the evaluation of the relative momentum
distribution and the Fermi sea depletion. We found that the value of the Fermi
sea depletion is higher in closed shell nuclei compared to open shell ones and
it is lower compared to the case of nuclear matter. This statement could be
confirmed by relevant experimental studies.Comment: 20 pages, 3 figures, 2 table
One-body density matrix and momentum distribution in s-p and s-d shell nuclei
Analytical expressions of the one- and two- body terms in the cluster expansion of the one-body density matrix and momentum distribution of the s-p and s-d shell nuclei with N=Z are derived. They depend on the harmonic oscillator parameter b and the parameter which originates from the Jastrow correlation function. These parameters have been determined by least squares fit to the experimental charge form factors. The inclusion of short-range correlations increases the high momentum component of the momentum distribution, for all nuclei we have considered while there is an A dependence of both at small values of k and the high momentum component. The A dependence of the high momentum component of becomes quite small when the nuclei Mg, Si and S are treated as 1d-2s shell nuclei having the occupation probability of the 2s-state as an extra free parameter in the fit to the form factors
Quantum Tunneling and Information Entropy in a Double Square Well Potential: Ammonia Molecule
Quantum tunneling is the quantum-mechanical effect where a particle tunnels
through a classically forbidden region. Double Square Well Potential (DSWP) is
a system where this phenomenon is feasible. Numerous phenomena can be
illustrated by considering motion in a pair of wells that are separated by a
barrier of finite height and width. The energy level splitting, resulting from
barrier penetration, is the reason of the so-called inversion spectrum, which
is an example of quantum tunneling. Out of several molecules (, ,
, ) where this inversion phenomenon occurs, ammonia molecule
provides a nice physical realization of a vibrational system with a
DSWP. The main goal of the present work is to examine the implications of
quantum tunneling on information entropy measures (Shannon's and Fisher's) and
statistical complexity.Comment: 16 pages, 15 figures, 2 table
Effects of the equation of state on the bulk properties of maximally-rotating neutron stars
Neutron stars are among the densest known objects in the universe and an
ideal laboratory for the strange physics of super-condensed matter. While the
simultaneously measurements of mass and radius of non-rotating neutron stars
may impose constraints on the properties of the dense nuclear matter, the
observation and study of maximally-rotating ones, close to the mass-shedding
limit, may lead to significantly further constraints. Theoretical predictions
allow neutron stars to rotate extremely fast (even more than ). However, until this moment, the fastest observed rotating pulsar has a
frequency of , much lower compared to the theoretical
predictions. There are many suggestions for the mechanism which lead to this
situation. In any case, the theoretical study of uniformly rotating neutron
stars, along with the accurate measurements, may offer rich information
concerning the high density part of the equation of state. In addition, neutron
stars through their evolution, may provide us with a criteria to determine the
final fate of a rotating compact star. Sensitivity of bulk neutron stars
properties on the equation of state at the mass-shedding limit are the main
subject of the present study.Comment: v1: 16 pages, 24 figures. v2: 18 pages, 14 labeled figures, 5 tables,
sections and references had been updated, accepted for publication in Phys.
Rev.
Fisher Information and Atomic Structure
We present a comparative study of several information and statistical
complexity measures in order to examine a possible correlation with certain
experimental properties of atomic structure. Comparisons are also carried out
quantitatively using Pearson correlation coefficient. In particular, we show
that Fisher information in momentum space is very sensitive to shell effects,
and is directly associated with some of the most characteristic atomic
properties, such as atomic radius, ionization energy, electronegativity, and
atomic dipole polarizability. Finally we present a relation that emerges
between Fisher information and the second moment of the probability
distribution in momentum space i.e. an energy functional of interest in (e,2e)
experiments.Comment: 8 pages, 5 figures; Corrected typo
Statistical measure of complexity of hard-sphere gas: applications to nuclear matter
We apply the statistical measure of complexity, introduced by L\'{o}pez-Ruiz,
Mancini and Calbet to a hard-sphere dilute Fermi gas whose particles interact
via a repulsive hard-core potential. We employ the momentum distribution of
this system to calculate the information entropy, the disequilibrium and the
statistical complexity. We examine possible connections between the particle
correlations and energy of the system with those information and complexity
measures. The hard-sphere model serves as a test bed for concepts about
complexity.Comment: 10 pages, 9 figure
Thermodynamical description of hot rapidly rotating neutron stars and neutron stars merger remnant
The prediction of the equation of state of hot dense nuclear matter is one of
the most complicated and interesting problems in Nuclear Astrophysics. At the
same time, its knowledge is the basic ingredient for some of the most
interesting studies. In the present work we concentrate our study on the
construction of the equation of state of hot dense nuclear matter, related
mainly to the interior of the neutron star core. We employ a theoretical
nuclear model, which includes momentum dependent interaction among the
nucleons, along with the \textit{state-of-the-art} microscopic calculations.
Thermal effects are introduced in a self-consistent way and a set of isothermal
equations of state are predicted. The predicted equations of state are used in
order to acquire and to extend the knowledge of thermal effect both on
non-rotating and rapidly rotating with the Kepler frequency neutron stars. The
simultaneously study of thermal and rotation effect provide useful information
for some of the most important quantities, including the mass (gravitational
and baryon) and radius, the Kepler frequency and kerr parameter, the moment of
inertia etc. These quantities are directly related to studies of proto-neutron
stars and mainly the hot and rapidly rotating remnant of a binary neutron stars
merger. Data from the late observations of binary neutron stars mergers and the
present study may offer useful tools for their investigation and help in
providing possible constraints on the equation of state of nuclear matter.Comment: 24 pages, 17 figures, 5 table
Applications of density matrices in a trapped Bose gas
An overview of the Bose-Einstein condensation of correlated atoms in a trap
is presented by examining the effect of interparticle correlations to one- and
two-body properties of the above systems at zero temperature in the framework
of the lowest order cluster expansion. Analytical expressions for the one- and
two-body properties of the Bose gas are derived using Jastrow-type correlation
function. In addition numerical calculations of the natural orbitals and
natural occupation numbers are also carried out. Special effort is devoted for
the calculation of various quantum information properties including Shannon
entropy, Onicescu informational energy, Kullback-Leibler relative entropy and
the recently proposed Jensen-Shannon divergence entropy. The above quantities
are calculated for the trapped Bose gases by comparing the correlated and
uncorrelated cases as a function of the strength of the short-range
correlations. The Gross-Piatevskii equation is solved giving the density
distributions in position and momentum space, which are employed to calculate
quantum information properties of the Bose gas.Comment: 40 pages, 14 figures, 2 Table
- …