Propriedades de transporte de energia em sistemas quânticos abertos: análise da cadeia XX e do modelo de Ising

Abstract

Transport phenomena are a major challenge that encourages researchers to to unravel the microscopic mechanisms that govern its properties. The development of quantum devices and theoretical tools to understand how open quantum systems works out of the equilibrium has received increasing attention in recent years and has demonstrated interesting thermodynamic properties, which lack attention in your definitions to avoid any physical contradictions. In this context, an important and recurrently studied transport property, with great experimental application, is the existence of rectification, that is, a preferential direction for the flow. In this present Thesis, aiming at the understanding of control mechanisms and manipulation of heat/work/spin currents and also the thermodynamic properties that quantum systems have, we carried out a detailed investigation into central models of study through two master equations in Lindblad form, known as Local Master Equation and Global Master Equation. We deduce the Local equation through Repeated Interaction Protocol and applied to the Ising model subject to two types of reservoirs in the ends, spin reservoir and thermal reservoir, in order to dismember the current of energy in its components: heat and work. This first approach elucidates thermodynamic consistency that this derivation has in addition to providing theoretical tools govern heat and work currents individually. We apply the Global equation, deducted through the Weak Coupling Limit Derivation, to the XX chain together with Jordan-Wigner transformations in order to deduce an fully analytical model which allowed us to demonstrate the existence of thermal rectification in this model, the which proved to be an excellent rectifier with non-zero rectification factor at the limit thermodynamic. We deepened the study of this system with the presence of dephasing in the model governed by the Lindblad Global equation aiming to understand the mechanisms to control and manipulate spin currents. We found that the interaction between dephasing and graded systems promoted an enhancement in the rectification factor of the spin current and we also saw that when we have a completely graded system it is possible to control the direction of the current, allowing it to flow in a single direction even with inverted reservoirs.