Chaotic behavior of the Compound Nucleus, open Quantum Dots and other nanostructures

It is well established that physical systems exhibit both ordered and chaotic behavior. The chaotic behavior of nanostructure such as open quantum dots has been confirmed experimentally and discussed exhaustively theoretically. This is manifested through random fluctuations in the electronic conductance. What useful information can be extracted from this noise in the conductance? In this contribution we shall address this question. In particular, we will show that the average maxima density in the conductance is directly related to the correlation function whose characteristic width is a measure of energy- or applied magnetic field- correlation length. The idea behind the above has been originally discovered in the context of the atomic nucleus, a mesoscopic system. Our findings are directly applicable to graphene.Comment: 10 pages, 5 figures. Contribution to: "4th International Workshop on Compound-Nuclear Reactions and Related Topics (CNR*13)", October 7-11, 2013, Maresias, Brazil. To appear in the proceeding

Hamming distance and mobility behavior in generalized rock-paper-scissors models

This work reports on two related investigations of stochastic simulations which are widely used to study biodiversity and other related issues. We first deal with the behavior of the Hamming distance under the increase of the number of species and the size of the lattice, and then investigate how the mobility of the species contributes to jeopardize biodiversity. The investigations are based on the standard rules of reproduction, mobility and predation or competition, which are described by specific rules, guided by generalization of the rock-paper-scissors game, valid in the case of three species. The results on the Hamming distance indicate that it engenders universal behavior, independently of the number of species and the size of the square lattice. The results on the mobility confirm the prediction that it may destroy diversity, if it is increased to higher and higher values.Comment: 7 pages, 9 figures. To appear in EP

Time-Reversal Symmetry Breaking and Decoherence in Chaotic Dirac Billiards

In this work, we perform a statistical study on Dirac Billiards in the extreme quantum limit (a single open channel on the leads). Our numerical analysis uses a large ensemble of random matrices and demonstrates the preponderant role of dephasing mechanisms in such chaotic billiards. Physical implementations of these billiards range from quantum dots of graphene to topological insulators structures. We show, in particular, that the role of finite crossover fields between the universal symmetries quickly leaves the conductance to the asymptotic limit of unitary ensembles. Furthermore, we show that the dephasing mechanisms strikingly lead Dirac billiards from the extreme quantum regime to the semiclassical Gaussian regime