Localização eletrônica de sistemas aperiódicos em uma dimensão

Desde a descoberta do estado quasicristalino por Daniel Shechtman et al. em 1984 e da fabricação por Roberto Merlin et al. de uma superrede artificial de GaAs/ AlAs em 1985 com características da sequência de Fibonacci, um grande número de trabalhos teóricos e experimentais tem relatado uma variedade de propriedades interessantes no comportamento de sistemas aperiódicos. Do ponto de vista teórico, é bem sabido que a cadeia de Fibonacci em uma dimensão se constitui em um protótipo de sucesso para a descrição do estado quasicristalino de um sólido. Dependendo da regra de inflação, diferentes tipos de estruturas aperiódicas podem ser obtidas. Esta diversidade originou as chamadas regras metálicas e devido à possibilidade de tratamento analítico rigoroso este modelo tem sido amplamente estudado. Neste trabalho, propriedades de localização em uma dimensão são analisadas considerando-se um conjunto de regras metálicas e o modelo de ligações fortes de banda única. Considerando-se o Hamiltoniano de ligações fortes com um orbital por sítio obtemos um conjunto de transformações relativas aos parâmetros de dizimação, o que nos permitiu calcular as densidades de estados (DOS) para todas as configurações estudadas. O estudo detalhado da densidade de estados integrada (IDOS) para estes casos, mostra o surgimento de plateaux na curva do número de ocupação explicitando o aparecimento da chamada escada do diabo" e também o caráter fractal destas estruturas. Estudando o comportamento da variação da energia em função da variação da energia de hopping, construímos padrões do tipo borboletas de Hofstadter, que simulam o efeito de um campo magnético atuando sobre o sistema. A natureza eletrônica dos auto estados é analisada a partir do expoente de Lyapunov (γ), que está relacionado com a evolução da função de onda eletrônica ao longo da cadeia unidimensional. O expoente de Lyapunov está relacionado com o inverso do comprimento de localização (ξ= 1 /γ), sendo nulo para os estados estendidos e positivo para estados localizados. Isto define claramente as posições dos principais gaps de energia do sistema. Desta forma, foi possível analisar o comportamento autossimilar de cadeias com diferentes regras de formação. Analisando-se o espectro de energia em função do número de geração de cadeias que seguem as regras de ouro e prata foi feito, obtemos conjuntos do tipo-Cantor, que nos permitiu estudar o perfil do calor específico de uma cadeia e Fibonacci unidimensional para diversas gerações

Synthesis and structural aspects of quasicrystals in Mg-Al-Ag system: Mg4Al6Ag

The existence of an icosahedral phase in Mg−Al−Ag is better understood on a crystallographic basis rather than on a quantum structural diagram basis. The quasicrystalline structure is delineated in terms of quasiperiodic arrangement of Pauling triacontahedra, which can be identified in the equilibrium structure. Subtle differences in the electron diffraction patterns have been recorded compared to the ideal quasicrystalline pattern. The misalignment of spots and distortions are better attributed to higher order rational approximate structure than anisotropic phason strain. Ares of diffuse intensity have been related to the ordering among the atoms in the clusters.

Single-photon source in strong photon-atom interaction regime in quasiperiodic photonic crystals

The antibunching properties of the fluorescence from a two-level ideal system in a 12-fold quasiperiodic photonic crystal are investigated based on the calculated local density of states. We found that the antibunching phenomenon of the fluorescence from two-level ideal systems could be significantly changed by varying their positions, i.e., perfect antibunching and antibunching with damped Rabi oscillation phenomenon occurred in different positions and at different frequencies in photonic crystals as a result of the large differences in the local density of states. This study revealed that the multi-level coherence of fluorescence from a two-level ideal system could be manipulated by controlling the position of the two-level ideal system in photonic crystals and the emission frequency in the photonic band structure. Copyright (C) EPLA, 2008

Chaotic vibrations of a nonideal electro-mechanical system

Nonideal systems are those in which one takes account of the influence of the oscillatory system on the energy supply with a limited power (Kononenko, 1969). In this paper, a particular nonideal system is investigated, consisting of a pendulum whose support point is vibrated along a horizontal guide by a two bar linkage driven by a DC motor, considered to be a limited power supply. Under these conditions, the oscillations of the pendulum are analyzed through the variation of a control parameter. The voltage supply of the motor is considered to be a reliable control parameter. Each simulation starts from zero speed and reaches a steady-state condition when the motor oscillates around a medium speed. Near the fundamental resonance region, the system presents some interesting nonlinear phenomena, including multi-periodic, quasiperiodic, and chaotic motion. The loss of stability of the system occurs through a saddle-node bifurcation, where there is a collision of a stable orbit with an unstable one, which is approximately located close to the value of the pendulum's angular displacement given by alpha (C)= pi /2. The aims of this study are to better understand nonideal systems using numerical simulation, to identify the bifurcations that occur in the system, and to report the existence of a chaotic attractor near the fundamental resonance. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Emergence of order in visual system development.

Neural connections in the adult central nervous system are highly precise. In the visual system, retinal ganglion cells send their axons to target neurons in the lateral geniculate nucleus (LGN) in such a way that axons originating from the two eyes terminate in adjacent but nonoverlapping eye-specific layers. During development, however, inputs from the two eyes are intermixed, and the adult pattern emerges gradually as axons from the two eyes sort out to form the layers. Experiments indicate that the sorting-out process, even though it occurs in utero in higher mammals and always before vision, requires retinal ganglion cell signaling; blocking retinal ganglion cell action potentials with tetrodotoxin prevents the formation of the layers. These action potentials are endogenously generated by the ganglion cells, which fire spontaneously and synchronously with each other, generating "waves" of activity that travel across the retina. Calcium imaging of the retina shows that the ganglion cells undergo correlated calcium bursting to generate the waves and that amacrine cells also participate in the correlated activity patterns. Physiological recordings from LGN neurons in vitro indicate that the quasiperiodic activity generated by the retinal ganglion cells is transmitted across the synapse between ganglion cells to drive target LGN neurons. These observations suggest that (i) a neural circuit within the immature retina is responsible for generating specific spatiotemporal patterns of neural activity; (ii) spontaneous activity generated in the retina is propagated across central synapses; and (iii) even before the photoreceptors are present, nerve cell function is essential for correct wiring of the visual system during early development. Since spontaneously generated activity is known to be present elsewhere in the developing CNS, this process of activity-dependent wiring could be used throughout the nervous system to help refine early sets of neural connections into their highly precise adult patterns.