Propriedades não triviais do fluxo de calor via modelos microscópicos

Abstract

In this dissertation, having in mind to understand and/or identify possible mechanisms to control and manipulate the heat flow, we search for non-trivial properties, with important practical applications, by performing analytical and numerical study of recurrent microscopic models used in the description of heat conduction, i.e., anharmonic and harmonic chains of oscillators coupled to two thermal reservoirs differentat the ends. First, we describe an insulating effect related to chains with alternate masses: roughly, we show that the conduction in a system with alternate masses is worse than in a system with particles with the same mass. We show that such property is present in three very different models, suggesting that it is a ubiquitous phenomenon. Moreover, inspired by some previous works of our research group and collaborators, we study the thermal rectification phenomenon and guarantee its existence from some assumptions for the local heat flow: i.e., from a local thermal conductivity dependent on temperature and the presence of some asymmetry in the system, besides the existence of a local temperature gradient. Furthermore, we evaluated how the rectification factor behaves with the temperature gradient. We recall that thermal rectification is the phenomenon in which the magnitude of heat current changes as we invert the thermal baths at the boundaries. Using the developed formalism, we show the existence of thermal rectification in a quantum harmonic chain of oscillators with self-consistent thermal reservoirs. We identify the necessary ingredients for its existence, and note that such ingredients are also found in classical anharmonic chains, showing that the occurrence of rectification is not constrained to the quantum nature of the system (but the analogue classical harmonic chain has no rectification). We also present a rigorous proof for the absence of rectification in this analogue classical harmonic chain. Finally, searching for mechanisms that can enhance the thermal rectification and/or avoid its decay as we increase the size of the system, we study the effect of long-range interactions in the heat flow and its relationship with the phenomenon of rectification. We find that, despite the difficulties associated with the study of heat conduction models with anharmonic potential (even for the case of nearest neighbor interactions), an investigation considering long-range interactions is possible. We show that, besides the amplification of the thermal conductivity and the change in the transport regime, we can increase the thermal rectification. Moreover, we present an example of a graded system, i.e., a system in which some structure monotonically changes (e.g., the particle mass or the on-site potential), where the rectification does not decay as we increase the system size. We emphasize that such decay of the rectification with the system size is one of the problems of the current models of thermal rectifiers: problem that we solve here with the addition of long-range interactions.