309 research outputs found
Preferential attachment during the evolution of a potential energy landscape
It has previously been shown that the network of connected minima on a
potential energy landscape is scale-free, and that this reflects a power-law
distribution for the areas of the basins of attraction surrounding the minima.
Here, we set out to understand more about the physical origins of these
puzzling properties by examining how the potential energy landscape of a
13-atom cluster evolves with the range of the potential. In particular, on
decreasing the range of the potential the number of stationary points increases
and thus the landscape becomes rougher and the network gets larger. Thus, we
are able to follow the evolution of the potential energy landscape from one
with just a single minimum to a complex landscape with many minima and a
scale-free pattern of connections. We find that during this growth process, new
edges in the network of connected minima preferentially attach to more
highly-connected minima, thus leading to the scale-free character. Furthermore,
minima that appear when the range of the potential is shorter and the network
is larger have smaller basins of attraction. As there are many of these smaller
basins because the network grows exponentially, the observed growth process
thus also gives rise to a power-law distribution for the hyperareas of the
basins.Comment: 10 pages, 10 figure
Quantum-Information Theoretic Properties of Nuclei and Trapped Bose Gases
Fermionic (atomic nuclei) and bosonic (correlated atoms in a trap) systems
are studied from an information-theoretic point of view. Shannon and Onicescu
information measures are calculated for the above systems comparing correlated
and uncorrelated cases as functions of the strength of short range
correlations. One-body and two-body density and momentum distributions are
employed. Thus the effect of short-range correlations on the information
content is evaluated. The magnitude of distinguishability of the correlated and
uncorrelated densities is also discussed employing suitable measures of
distance of states i.e. the well known Kullback-Leibler relative entropy and
the recently proposed Jensen-Shannon divergence entropy. It is seen that the
same information-theoretic properties hold for quantum many-body systems
obeying different statistics (fermions and bosons).Comment: 24 pages, 9 figures, 1 tabl
Effects of Short Range Correlations on Ca Isotopes
The effect of Short Range Correlations (SRC) on Ca isotopes is studied using
a simple phenomenological model. Theoretical expressions for the charge
(proton) form factors, densities and moments of Ca nuclei are derived. The role
of SRC in reproducing the empirical data for the charge density differences is
examined. Their influence on the depletion of the nuclear Fermi surface is
studied and the fractional occupation probabilities of the shell model orbits
of Ca nuclei are calculated. The variation of SRC as function of the mass
number is also discussed.Comment: 11 pages (RevTex), 6 Postscript figures available upon request at
[email protected] Physical Review C in prin
Universal trend of the information entropy of a fermion in a mean field
We calculate the information entropy of single-particle states in
position-space and momentum-space for a nucleon in a nucleus, a
particle in a hypernucleus and an electron in an atomic cluster. It
is seen that and obey the same approximate functional form as
functions of the number of particles, ({\rm or}
in all of the above many-body systems in position- and momentum- space
separately. The net information content is a slowly varying
function of of the same form as above. The entropy sum is
invariant to uniform scaling of coordinates and a characteristic of the
single-particle states of a specific system. The order of single-particle
states according to is the same as their classification according to
energy keeping the quantum number constant. The spin-orbit splitting is
reproduced correctly. It is also seen that enhances with
excitation of a fermion in a quantum-mechanical system. Finally, we establish a
relationship of with the energy of the corresponding single-particle
state i.e. . This relation holds for all the
systems under consideration.Comment: 9 pages, latex, 6 figure
Characterizing the network topology of the energy landscapes of atomic clusters
By dividing potential energy landscapes into basins of attractions
surrounding minima and linking those basins that are connected by transition
state valleys, a network description of energy landscapes naturally arises.
These networks are characterized in detail for a series of small Lennard-Jones
clusters and show behaviour characteristic of small-world and scale-free
networks. However, unlike many such networks, this topology cannot reflect the
rules governing the dynamics of network growth, because they are static spatial
networks. Instead, the heterogeneity in the networks stems from differences in
the potential energy of the minima, and hence the hyperareas of their
associated basins of attraction. The low-energy minima with large basins of
attraction act as hubs in the network.Comparisons to randomized networks with
the same degree distribution reveals structuring in the networks that reflects
their spatial embedding.Comment: 14 pages, 11 figure
Systematic study of the effect of short range correlations on the form factors and densities of s-p and s-d shell nuclei
Analytical expressions of the one- and two-body terms in the cluster
expansion of the charge form factors and densities 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 expressions are used for the systematic study of the effect of
short range correlations on the form factors and densities and of the mass
dependence of the parameters b and . These parameters have been
determined by fit to the experimental charge form factors. The inclusion of the
correlations reproduces the experimental charge form factors at the high
momentum transfers (). It is found that while the parameter
is almost constant for the closed shell nuclei, He, O and
Ca, its values are larger (less correlated systems) for the open shell
nuclei, indicating a shell effect in the closed shell nuclei.Comment: Latex, 21 pages, 6 figures, 1 tabl
Testing He density distributions by calculations of total reaction cross-sections of He+Si
Calculations of the He + Si total reaction cross sections at
intermediate energies are performed on the basis of the Glauber-Sitenko
microscopic optical-limit model. The target-nucleus density distribution is
taken from the electron-nucleus scattering data, and the He densities
are used as they are derived in different models. The results of the
calculations are compared with the existing experimental data. The effects of
the density tails of the projectile nuclei as well as the role of shell
admixtures and short-range correlations are analyzed.Comment: 10 pages, 5 figures. Submitted to the International Journal of Modern
Physics
Size reduction of complex networks preserving modularity
The ubiquity of modular structure in real-world complex networks is being the
focus of attention in many trials to understand the interplay between network
topology and functionality. The best approaches to the identification of
modular structure are based on the optimization of a quality function known as
modularity. However this optimization is a hard task provided that the
computational complexity of the problem is in the NP-hard class. Here we
propose an exact method for reducing the size of weighted (directed and
undirected) complex networks while maintaining invariant its modularity. This
size reduction allows the heuristic algorithms that optimize modularity for a
better exploration of the modularity landscape. We compare the modularity
obtained in several real complex-networks by using the Extremal Optimization
algorithm, before and after the size reduction, showing the improvement
obtained. We speculate that the proposed analytical size reduction could be
extended to an exact coarse graining of the network in the scope of real-space
renormalization.Comment: 14 pages, 2 figure
Calculations of He+p Elastic Cross Sections Using Microscopic Optical Potential
An approach to calculate microscopic optical potential (OP) with the real
part obtained by a folding procedure and with the imaginary part inherent in
the high-energy approximation (HEA) is applied to study the He+p elastic
scattering data at energies of tens of MeV/nucleon (MeV/N). The neutron and
proton density distributions obtained in different models for He are
utilized in the calculations of the differential cross sections. The role of
the spin-orbit potential is studied. Comparison of the calculations with the
available experimental data on the elastic scattering differential cross
sections at beam energies of 15.7, 26.25, 32, 66 and 73 MeV/N is performed. The
problem of the ambiguities of the depths of each component of the optical
potential is considered by means of the imposed physical criterion related to
the known behavior of the volume integrals as functions of the incident energy.
It is shown also that the role of the surface absorption is rather important,
in particular for the lowest incident energies (e.g., 15.7 and 26.25
MeV/nucleon).Comment: 11 pages, 7 figures, accepted for publication in Physical Review
Information entropy as a measure of the quality of a nuclear density distribution
The information entropy of a nuclear density distribution is calculated for a
number of nuclei. Various phenomenological models for the density distribution
using different geometry are employed. Nuclear densities calculated within
various microscopic mean field approaches are also employed. It turns out that
the entropy increases on going from crude phenomenological models to more
sophisticated (microscopic) ones. It is concluded that the larger the
information entropy, the better the quality of the nuclear density
distribution. An alternative approach is also examined: the net information
content i.e. the sum of information entropies in position and momentum space
. It is indicated that is a maximum, when the best
fit to experimental data of the density and momentum distributions is attained.Comment: 12 pages, LaTex, no figures, Int. J. of Mod. Phys. E in pres
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