Shape of Traveling Densities with Extremum Statistical Complexity

In this paper, we analyze the behavior of statistical complexity in several systems where two identical densities that travel in opposite direction cross each other. Besides the crossing between two Gaussian, rectangular and triangular densities studied in a previous work, we also investigate in detail the crossing between two exponential and two gamma distributions. For all these cases, the shape of the total density presenting an extreme value in complexity is found.Comment: 11 pages, 14 figure

Statistical measures and the Klein tunneling in single-layer graphene

Statistical complexity and Fisher-Shannon information are calculated in a problem of quantum scattering, namely the Klein tunneling across a potential barrier in graphene. The treatment of electron wave functions as masless Dirac fermions allows us to compute these statistical measures. The comparison of these magnitudes with the transmission coefficient through the barrier is performed. We show that these statistical measures take their minimum values in the situations of total transparency through the barrier, a phenomenon highly anisotropic for the Klein tunneling in graphene.Comment: 10 pages, 4 figure

Statistical measures applied to metal clusters: evidence of magic numbers

In this work, a shell model for metal clusters up to 220 valence electrons is used to obtain the fractional occupation probabilities of the electronic orbitals. Then, the calculation of a statistical measure of complexity and the Fisher-Shannon information is carried out. An increase of both magnitudes with the number of valence electrons is observed. The shell structure is reflected by the behavior of the statistical complexity. The magic numbers are indicated by the Fisher-Shannon information. So, as in the case of atomic nuclei, the study of statistical indicators also unveil the existence of magic numbers in metal clusters.Comment: 7 pages, 3 figure

Evidence of magic numbers in nuclei by statistical indicators

The calculation of a statistical measure of complexity and the Fisher-Shannon information in nuclei is carried out in this work. We use the nuclear shell model in order to obtain the fractional occupation probabilities of nuclear orbitals. The increasing of both magnitudes, the statistical complexity and the Fisher-Shannon information, with the number of nucleons is observed. The shell structure is reflected by the behavior of the statistical complexity. The magic numbers are revealed by the Fisher-Shannon information.Comment: 7 pages, 2 figure

Heisenberg uncertainty relation and statistical measures in the square well

A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are calculated with time for this system. These measures are compared with the Heisenberg uncertainty relation, \Delta x\Delta p. It is observed that the extreme values of \Delta x\Delta p coincide in time with extreme values of the other two statistical magnitudes.Comment: 7 pages, 4 figure

Alternative evaluation of statistical indicators in atoms: the non-relativistic and relativistic cases

In this work, the calculation of a statistical measure of complexity and the Fisher-Shannon information is performed for all the atoms in the periodic table. Non-relativistic and relativistic cases are considered. We follow the method suggested in [C.P. Panos, N.S. Nikolaidis, K. Ch. Chatzisavvas, C.C. Tsouros, arXiv:0812.3963v1] that uses the fractional occupation probabilities of electrons in atomic orbitals, instead of the continuous electronic wave functions. For the order of shell filling in the relativistic case, we take into account the effect due to electronic spin-orbit interaction. The increasing of both magnitudes, the statistical complexity and the Fisher-Shannon information, with the atomic number $Z$ is observed. The shell structure and the irregular shell filling is well displayed by the Fisher-Shannon information in the relativistic case.Comment: 8 pages, 4 figure

Statistical Complexity in Traveling Densities

In this work, we analyze the behavior of statistical complexity in several systems where two identical densities that travel in opposite direction cross each other. The crossing between two Gaussian, rectangular and triangular densities is studied in detail. For these three cases, the shape of the total density presenting an extreme value in complexity is found.Comment: 4 pages, 7 figure

Complexity invariance by replication in the quantum square well

A new kind of invariance by replication of a statistical measure of complexity is considered. We show that the set of energy eigenstates of the quantum infinite square well displays this particular invariance. Then, this system presents a constant complexity for all the energy eigenstates.Comment: 5 pages, 0 figure

Study of a quantum scattering process by means of entropic measures

In this work, a scattering process of quantum particles through a potential barrier is considered. The statistical complexity and the Fisher-Shannon information are calculated for this problem. The behaviour of these entropy-information measures as a function of the energy of the incident particles is compared with the behaviour of a physical magnitude, the reflection coefficient in the barrier. We find that these statistical magnitudes present their minimum values in the same situations in which the reflection coefficient is null. These are the situations where the total transmission through the barrier is achieved, {\it the transparency points}, a typical phenomenon due to the quantum nature of the system.Comment: 9 pages, 4 figure

Equilibrium Distributions in Open and Closed Statistical Systems

In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by working out the properties of the volume or the surface of the respective geometries delimited in phase space by an additive constraint. That is, the asymptotic equilibrium distributions in the thermodynamic limit are independent of considering open or closed homogeneous statistical systems.Comment: 5 pages, 0 figure