The problem of the Klein tunneling across a potential barrier in bi-layer graphene is addressed. The electron wave functions are treated as massive chiral particles. This treatment allows us to compute the statistical complexity and Fisher-Shannon in
formation for each angle of incidence. The comparison of these magnitudes with the transmission coefficient through the barrier is performed. The role played by the evanescent waves on these magnitudes is disclosed. Due to the influence of these waves, it is found that the statistical measures take their minimum values not only in the situations of total transparency through the barrier, a phenomenon highly anisotropic for the Klein tunneling in bi-layer graphene.
An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of money has recently been proposed by one of us (RLR). This equation takes the form of an iterated
nonlinear map of the distribution of wealth. The equilibrium distribution is known and takes a rather simple form. If this distribution is such that, at some time, the higher momenta of the distribution exist, one can find exactly their law of evolution. A seemingly simple extension of the laws of exchange yields also explicit iteration formulae for the higher momenta, but with a major difference with the original iteration because high order momenta grow indefinitely. This provides a quantitative model where the spreading of wealth, namely the difference between the rich and the poor, tends to increase with time.
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 t
o 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.
In general, the behavior of large and complex aggregates of elementary components can not be understood nor extrapolated from the properties of a few components. The brain is a good example of this type of networked systems where some patterns of beh
avior are observed independently of the topology and of the number of coupled units. Following this insight, we have studied the dynamics of different aggregates of logistic maps according to a particular {it symbiotic} coupling scheme that imitates the neuronal excitation coupling. All these aggregates show some common dynamical properties, concretely a bistable behavior that is reported here with a certain detail. Thus, the qualitative relationship with neural systems is suggested through a naive model of many of such networked logistic maps whose behavior mimics the waking-sleeping bistability displayed by brain systems. Due to its relevance, some regions of multistability are determined and sketched for all these logistic models.
We calculate a measure of statistical complexity from the global dynamics of electroencephalographic (EEG) signals from healthy subjects and epileptic patients, and are able to stablish a criterion to characterize the collective behavior in both grou
ps of individuals. It is found that the collective dynamics of EEG signals possess relative higher values of complexity for healthy subjects in comparison to that for epileptic patients. To interpret these results, we propose a model of a network of coupled chaotic maps where we calculate the complexity as a function of a parameter and relate this measure with the emergence of nontrivial collective behavior in the system. Our results show that the presence of nontrivial collective behavior is associated to high values of complexity; thus suggesting that similar dynamical collective process may take place in the human brain. Our findings also suggest that epilepsy is a degenerative illness related to the loss of complexity in the brain.
In this work, an ensemble of economic interacting agents is considered. The agents are arranged in a linear array where only local couplings are allowed. The deterministic dynamics of each agent is given by a map. This map is expressed by two factors
. The first one is a linear term that models the expansion of the agents economy and that is controlled by the {it growth capacity parameter}. The second one is an inhibition exponential term that is regulated by the {it local environmental pressure}. Depending on the parameter setting, the system can display Pareto or Boltzmann-Gibbs behavior in the asymptotic dynamical regime. The regions of parameter space where the system exhibits one of these two statistical behaviors are delimited. Other properties of the system, such as the mean wealth, the standard deviation and the Gini coefficient, are also calculated.
