Violação da teoria de escala em sistemas unidimensionais com desordem diluída e sistemas com acoplamentos de longo-alcance

• Ano de defesa: 2006
• Autor(a) principal: Albuquerque, Samuel Silva de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Alagoas; BR; Física geral; Física teórica e computacional; Mecânica estatística; Ótica; Ótica não linear; Proprie; Programa de Pós-Graduação em Física da Matéria Condensada; UFAL
• Palavras-chave em Português: Modelo de Anderson; Desordem; Percolação; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA
• Link de acesso: http://repositorio.ufal.br/handle/riufal/1010

In random non-interacting electron systems in three-dimensional lattices with uncorrelated disorder, it has been well established that there is a metal-insulator transition, usually named Anderson transition, in which the one-electron eigenstates change their nature from extended to localized as a function of the disorder strength. In low-dimensional systems with d &#8804; 2, the scaling theory of localization predicts complete localization for any strength of the disorder. In recent years, several studies in d = 1 and d = 2 have shown a violation of the scaling theory of localization if disorder has special correlations or the system presents long-range couplings. In this work, we analyze some one-dimensional systems that do present extended states. We study the one-electron wave-packet dynamics in the one-dimensional diluted Anderson model. The disorder is diluted by introducing between each pair of random sites a new site with fixed potential. This model presents extended states in particular resonant energies which leads to a very interesting phenomena of sensitivity to the initial condition of wave-packet spread. When the electron is initially localized in a diluting site, the wave-packet presents a faster spreading than that exhibited by a wave-packet initially localized in an Anderson site. Further, we explore the exact mapping between the one-electron eigen-states of tight-binding models onto the normal vibrational modes of harmonic chains to study the nature of collective excitations in harmonics chains with diluted disorder of the mass distribution. This model presents an extended harmonic state at &#969;c with null displacement at the random masses. For a initial pulse excitation, a super-diffusive energy spread is observed, similar to the one occurring in fully disordered chains. On the other hand, for an initial displacement excitation, the energy spreads diffusively, in contrast with the slower sub-diffusive spread in fully random chains. Finally, we study the classical and quantum percolation phenomena in power-law diluted chains for which the probability of occurrence of a bond between sites separated by a distance r decays a p(r) = p/r1+_. We present the phase diagram for both classical and quantum models for the range of the decay exponent 0 < &#963; < 1. In the case of classical percolation, we explore the scaling behavior of the mass of the largest clusters to obtain the critical parameters. We found that the critical percolation probability p grows continuously towards pc(&#963; = 1) = 1. Therefore, for coupling probabilities decaying with the square of the distance, the largest cluster is finite for any degree of dilution. The fractal dimension of the percolating cluster was estimated and displays two distinct regimes for &#963; < 1/2 and &#963; > 1/2. In the limit &#963; = 0 the fractal dimension is finite and converges to Df = 1 for &#963; = 1. Performing an exact diagonalization of the Hamiltonian of finite chains and using the scaling hypothesis, we investigate also the quantum percolation transition in the spanning cluster. Our results show the existence of a phase at which the one-electron eigenstates remain exponentially localized which means that the critical percolation probability for quantum percolation is larger than that for classical percolation. Finnaly, we found that the phase of extended states appears for &#963; < 0.78. This limiting value is larger than the one reported in the literature for the emergence of extended states in Anderson models in chains with power-law decaying couplings. Therefore, the present results indicate that there is not a direct correspondence between the quantum percolation and Anderson transition in chains with long-range couplings.