Estudo microscópico do fluxo de calor: abordagem analítica de sistemas de osciladores Classicos

Abstract

In this thesis we will study analytically the heat ow in a chain of anharmonic oscillators. Initially, we introduce a microscopic model with oscillators submitted to on-site anharmonic potentials and external and internal stochastic baths modeling sources of heat and anharmonicity. We develop an integral representation of the ow in terms of the correlation functions of stochastic variables over non-gaussian measures. Due to the great diculty of treating the expressions, we make diferent approaches to obtain analytical results related to the heat transport. In a rst approach, it is made a time discretization, which allows an explicit calculation of the ow by perturbative analysis with a non-gaussian single spin distribution. Such perturbative analysis is then justied rigorously by a polymer expansion for the model, whose convergence is proven. It is expected that the results signicantly represent the original model with only minor corrections. Another problem is treated with a second approach: the anharmonicity is replaced by an average value of the eld in order to obtain a linear dynamic. From this approach, the heat ow is calculated as a function of the temperatures and is observed the presence of NDTR (negative dierential thermal resistence) analytically under a specic regime, showing that the phenomenon does not need dierent conditions that appear in the literature