Estudo da condução de calor em modelos microscópicos via coordenadas no espaço recíproco - Ricardo Ribeiro de Avila (2009)
We work with Hamiltonian models out of thermal equilibrium. We use stochastic noise to model the contact system with the thermal reservoirs. We review some results from the literature mainly for cases where the stochastic dynamics is linear. The solution of these problems depends of the linearity system, it is impossible a direct extension to cases where there is an anharmonic system. We review also the integral representation developed by the group for processing the heat flow from 1- dimensional chain in the position space. We study the problem of heat flow in microscopic models using coordinates in reciprocal space. We consider the problem with periodic boundary conditions (in the literature) and Dirichlet conditions (natural to the problem of a system subjected totwo different thermal reservoirs at its ends). Show differences in expression (Hamiltonian, heat flux) for both conditions. From dynamics analysis in reciprocal space, we propose a new model by modifyingthe noise associated with stochastic dynamics in this space. Therefore we construct an integral representation for the correlation functions treatment of coordinates which are combinations of real variables defined in the wave vectors space. The great advantage of formalism building in this space instead positions space formalism is that ourmodel depends on only two temperatures. The search for a new model even approximate or effective for the heat flow treatment into a chain of size N, becomes necessary because we do not yet know solved the problem of a anharmonic Hamiltonian with reservoirs only at the ends.