Transporte quântico de carga, spin e calor em nanoestruturas caóticas - Gomes, Anderson Alexandre Vieira (2016)
The Landauer-Büttiker matrix formulation is one of the main tools used on the mesoscopic physics to describe systems whose behavior is the same like the nuclear ones, specially concerns to the ressonances presentes on the decays processes when they are bombarded. In this work, we study the random matrix theory to justify continuity conditions presents on the mesoscopic systems in charge transport phenomena. Next, we are take the systems boundary conditions in apropriate scale and we use the ideas of matricial scattering formulation to derive the Mahaux-Weindermüller formula and nd the structure of the scattering matrix to systems in the lenght scale under consideration. With possession of this scattering matrix, we have analyzed the quantum transport conditions of eletric charge for systems at null temperature. Next, we have expand our analysis investigating this systems at not null temperature, leading to emergence of unconventional e ects, as happens in the spins Seebeck e ect, for instance. Later, we use a random matrix numerical implementation to represents the Wigner's ensembles to take back speci cs results of the same papers that presents results related to this work. This was the way to test the method and demonstrate their e ectiveness. Finally, also through numerical implementation where we used an ensemble with 4998 random matrix, we have analyzed the channels quantum transport for spins, investigating their correlations to note that, starting of the generating functions, it is possible to nd the statistical cumulants that allow us analyze transport observables, both in the semi classical regime (where there are larger number of the open scattering channels), as in the extreme quantum regime (where the number of the open scattering channels is small).