16 research outputs found
Universal property of the information entropy in fermionic and bosonic systems
It is shown that a similar functional form holds approximately
for the information entropy S as function of the number of particles N for
atoms, nuclei and atomic clusters (fermionic systems) and correlated
boson-atoms in a trap (bosonic systems). It is also seen that rigorous
inequalities previously found to hold between S and the kinetic energy T for
fermionic systems, hold for bosonic systems as well. It is found that
Landsberg's order parameter is an increasing function of N for the
above systems. It is conjectured that the above properties are universal i.e.
they do not depend on the kind of constituent particles (fermions or correlated
bosons) and the size of the system.Comment: 6 pages, 2 EPS figures, LaTe
Universal property of the information entropy in atoms, nuclei and atomic clusters
The position- and momentum-space information entropies of the electron
distributions of atomic clusters are calculated using a Woods-Saxon single
particle potential. The same entropies are also calculated for nuclear
distributions according to the Skyrme parametrization of the nuclear mean
field. It turns out that a similar functional form S=a+b ln N for the entropy
as function of the number of particles N holds approximately for atoms, nuclei
and atomic clusters. It is conjectured that this is a universal property of a
many-fermion system in a mean field. It is also seen that there is an analogy
of our expression for S to Boltzmann's thermodynamic entropy S=k ln W.Comment: 3 pages, REVTEX, one figur
Application of information entropy to nuclei
Shannon's information entropies in position- and momentum- space and their
sum are calculated for various - and - shell nuclei using a
correlated one-body density matrix depending on the harmonic oscillator size
and the short range correlation parameter which originates from a
Jastrow correlation function. It is found that the information entropy sum for
a nucleus depends only on the correlation parameter through the simple
relation , where , and
depend on the mass number . A similar approximate expression
is also valid for the root mean square radius of the nucleus as function of
leading to an approximate expression which connects with the root mean
square radius. Finally, we propose a method to determine the correlation
parameter from the above property of as well as the linear dependence of
on the logarithm of the number of nucleons.Comment: 10 pages, 10 EPS figures, RevTeX, Phys.Rev.C accepted for publicatio
Net Fisher information measure versus ionization potential and dipole polarizability in atoms
The net Fisher information measure, defined as the product of position and
momentum Fisher information measures and derived from the non-relativistic
Hartree-Fock wave functions for atoms with Z=1-102, is found to correlate well
with the inverse of the experimental ionization potential. Strong direct
correlations of the net Fisher information are also reported for the static
dipole polarizability of atoms with Z=1-88. The complexity measure, defined as
the ratio of the net Onicescu information measure and net Fisher information,
exhibits clearly marked regions corresponding to the periodicity of the atomic
shell structure. The reported correlations highlight the need for using the net
information measures in addition to either the position or momentum space
analogues. With reference to the correlation of the experimental properties
considered here, the net Fisher information measure is found to be superior
than the net Shannon information entropy.Comment: 16 pages, 6 figure
A simple method for the evaluation of the information content and complexity in atoms. A proposal for scalability
We present a very simple method for the calculation of Shannon, Fisher,
Onicescu and Tsallis entropies in atoms, as well as SDL and LMC complexity
measures, as functions of the atomic number Z. Fractional occupation
probabilities of electrons in atomic orbitals are employed, instead of the more
complicated continuous electron probability densities in position and momentum
spaces, used so far in the literature. Our main conclusions are compatible with
the results of more sophisticated approaches and correlate fairly with
experimental data. We obtain for the Tsallis entropic index the value q=1.031,
which shows that atoms are very close to extensivity. A practical way towards
scalability of the quantification of complexity for systems with more
components than the atom is indicated. We also discuss the issue if the
complexity of the electronic structure of atoms increases with Z. A Pair of
Order-Disorder Indices (PODI), which can be introduced for any quantum
many-body system, is evaluated in atoms. We conclude that "atoms are ordered
systems, which do not grow in complexity as Z increases".Comment: Preprint, 25 pages, 15 figures, 1 Tabl
Configuration Complexities of Hydrogenic Atoms
The Fisher-Shannon and Cramer-Rao information measures, and the LMC-like or
shape complexity (i.e., the disequilibrium times the Shannon entropic power) of
hydrogenic stationary states are investigated in both position and momentum
spaces. First, it is shown that not only the Fisher information and the
variance (then, the Cramer-Rao measure) but also the disequilibrium associated
to the quantum-mechanical probability density can be explicitly expressed in
terms of the three quantum numbers (n, l, m) of the corresponding state.
Second, the three composite measures mentioned above are analytically,
numerically and physically discussed for both ground and excited states. It is
observed, in particular, that these configuration complexities do not depend on
the nuclear charge Z. Moreover, the Fisher-Shannon measure is shown to
quadratically depend on the principal quantum number n. Finally, sharp upper
bounds to the Fisher-Shannon measure and the shape complexity of a general
hydrogenic orbital are given in terms of the quantum numbers.Comment: 22 pages, 7 figures, accepted i
Complexity and neutron stars structure
We apply the statistical measure of complexity introduced by Lopez-Ruiz,
Mancini and Calbet to neutron stars structure. Neutron stars is a classical
example where the gravitational field and quantum behavior are combined and
produce a macroscopic dense object. Actually, we continue the recent
application of Sanudo and Pacheco to white dwarfs structure. We concentrate our
study on the connection between complexity and neutron star properties, like
maximum mass and the corresponding radius, applying a specific set of realistic
equation of states. Moreover, the effect of the strength of the gravitational
field on the neutron star structure and consequently on the complexity measure
is also investigated. It is seen that neutron stars, consistent with
astronomical observations so far, are ordered systems (low complexity), which
cannot grow in complexity as their mass increases. This is a result of the
interplay of gravity, the short-range nuclear force and the very short-range
weak interaction.Comment: Preprint, 23 pages, 28 figure
The relative probability for the recoilless DELTA-production in nuclei in the plane wave impulse approximation
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