The Axelrod model for the dissemination of culture exhibits a rich spatial distribution of cultural domains, which depends on the values of the two model parameters: F , the number of cultural features and q, the common number of states each feature can assume. In the one-dimensional model with F = q = 2, which is closely related to the constrained voter model, Monte Carlo simulations indicate the existence of multicultural absorbing configurations in which at least one macroscopic domain coexist with a multitude of microscopic ones in the thermodynamic limit. However, rigorous analytical results for the infinite system starting from the configuration where all cultures are equally likely show convergence to only monocultural or consensus configurations. Here we show that this disagreement is due simply to the order that the time-asymptotic limit and the thermodynamic limit are taken in the simulations. In addition, we show how the consensus-only result can be derived using Monte Carlo simulations of finite chains.

Within the many different models that appeared with the use of cold atoms to design BECs the bubble trap shaped potential has been of great interest. For the anisotropic bubble trap physics in the thin-shell limit the relationship between the physical parameters and the resulting manifold geometry is yet to be fully understood. In this paper, we work towards this goal showing how the parameters of the system must be manipulated in order to allow for a non-collapsing thin-shell limit. In such a limit, a dimensional compactification takes place thus leading to an effective 2D Hamiltonian which relates to up-to-date bubble trap experiments. At last, our Hamiltonian is pertubatively solved for some particular cases as applications of our theory.

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Gostaria de agradecer meu orientador, professor Dr. Francisco Ednilson Alves dos Santos, que me orientou, guiou e aconselhou durante todo o período de nosso trabalho.Com seu conhecimento, paciência e incrível capacidade de enxergar a física do problema, ajudou-me deveras e permitiu que pudéssemos realizar esse trabalho. Também gostaria de agradecer o Dr. Vanderlei Salvador Bagnato, que nos apresentou em um momento difícil de meu doutorado e, praticamente, salvou minha carreira, introduzindo-me em seu grupo de átomos frios.