Efeitos de simetrias da equação de Lindblad no transporte quântico

Abstract

The understanding of non equilibrium quantum systems and, more specifically, of properties of their energy and spin currents has not only a great theoretical interest but also a technological one. In this dissertation, we will clarify the importance of this area by studying certain models that, although simple, already present the occurrence of interesting phenomena. We studied one-dimensional spin chains from the Heisenberg model and XXZ model with a graded structure that are coupled with reservoirs that tend to fix the edge spins in certain directions (target polarization). The rectification of the energy and spin currents and the recent discovered “one-way street” phenomenon [1] were analyzed in view of the conditions necessary for its emergence and maintenance. The latter, which consists in the absence of change of direction of the energy current when the baths are inverted, can initially seems to lead to a violation of the second law of thermodynamics but this is not the case because the energy current consists not only of a contribution due to heat but also one due to work [2–4] this leads us to a parallel with the emergent field of study of quantum thermodynamics that also was discussed briefly. In particular, the use of symmetries of the Lindblad equation was made in the deduction of the existence of those phenomena which allowed that the results found were independent of the transport regime and the size of the chain. Moreover, other interesting phenomena already described in the literature found through this approach were also presented. Finally, as an original result from the author, with a paper published in EPL (Europhysics Letters), the one-way street phenomenon has been extended to more general baths (but still target polarization) with pair of polarization that include directions with arbitrary angles on one side relative to a fixed direction on the other.