Análise do comportamento crítico de modelos de não-equilíbrio na presença de voos de Lévy

• Autor(a) principal: Anjos, Fabiana Carvalho dos
• Data de Publicação: 2020
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal de Alagoas (UFAL)
• Texto Completo: http://www.repositorio.ufal.br/handle/riufal/7596
• topic: Transições de fase; Expoentes críticos; Voos de Lévy; Phase transition; Critical exponents; Lévy flights; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA

In the present in the present work we investigate continuous phase transitions of nonequilibrium in models with diffusion, branching and annihilation processes. Initially, we consider a parity conserving model of branching and annihilating random walkers with long-range diffusion. We obtained the set of critical exponents associated to the growth in the number particles and its fluctuations, as well as the second- order moment ratio. Diffusion and branching processes are controlled by a diffusion probability p and the flight distance follows a Lévy distribution with exponent α. Three regimes were identified, in function of the Lévy exponent α: for α ≤ 5/2 infinitesimal branching is relevant and leads to an explosive growth of the particle number (a phase transition takes place for α > 5/2); short-range power-law scaling occurs for α > 7/2; in the intermediate regime (3/2 < α < 7/2), continuously varying exponents. In another contribution, we study the dynamics of the branching and annihilating process with long-range interactions. Static particles generate an offspring and annihilate upon contact. The branching distance is supposed to follow a Lévy-like power law distribution. We analyze the long term behavior of the mean particles number and its fluctuations as a function of the parameter α that controls the range of the branching process. We show that the dynamic exponente associated with the particle number fluctuations varies continuously for α < 4, while the particle number exponent only changes for α < 3. We report extreme value distributions, Frechet ( for α = 3) e Gumbell (for 2 < α < 3). For α > 3, Gaussian distributions were observed. We use Monte Carlo simulations.