This Thesis is concerned with the quasiclassical theory of meso-scopic superconductivity. The aim of the Thesis is to introduce the boundary conditions for a quasiclassical Green’s function on partially transparent interfaces in mesoscopic superconducting structures and to analyze the range of applicability of the quasiclassical theory. The linear boundary conditions for Andreev amplitudes, factoring the quasiclassical Green’s function, are presented.  The quasiclassical theory on classical trajectories is reviewed and then generalized to include knots with paths intersections.  The main focus of the Thesis is on the range of validity of the quasiclassical theory. This goal is achieved by comparison of quasiclassical and exact Green’s functions.  The exact Gor’kov Greens function cannot be directly used for the comparison because of its strong microscopic variations on the length-scale of λF. It is the coarse-grain averaged exact Green’s function which is appropriate for the comparison. In most of the typical cases the calculations show very good agreement between both theories. Only for certain special situations, where the classical trajectory contains loops, one encounters discrepancies. The numerical and analytical analysis of the role of the loop-like structures and their influence on discrepancies between both exact and quasiclassical approaches is one of the main results of the Thesis. It is shown that the terms missing in the quasiclassical theory can be attributed to the loops formed by the interfering paths.  In typical real samples any imperfection on the scale larger than the Fermi wavelength disconnects the loops and the path is transformed into the tree-like graph. It is concluded that the quasiclassical theory is fully applicable in most of real mesoscopic samples. In the situations where the conventional quasiclassical theory is inapplicable due to contribution of the interfering path, one can use the modification of the quasiclassical technique suggested in the Thesis.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-02-09T18:25:19Z No. of bitstreams: 1 franciscodefreitasabreu.pdf: 1020647 bytes, checksum: c0554d2b4af5e0e53222c98e83705fc4 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-03-19T18:03:55Z (GMT) No. of bitstreams: 1 franciscodefreitasabreu.pdf: 1020647 bytes, checksum: c0554d2b4af5e0e53222c98e83705fc4 (MD5) / Made available in DSpace on 2018-03-19T18:03:55Z (GMT). No. of bitstreams: 1 franciscodefreitasabreu.pdf: 1020647 bytes, checksum: c0554d2b4af5e0e53222c98e83705fc4 (MD5) Previous issue date: 2017-05-19 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Processos de transferência de energia em conlisões moleculares constituem uma área de grande interesse no ramo científico. Com este fomento, investigamos o processo de relaxação e ativação vibracional quando estudamos a colisão não reativa entre N2 e H2, com 10kcal/mol ≤ Etr ≤ 100kcal/mol, encontrando computacionalmente distribuições vibracionais Digite a equação aqui.do N2, a fim de obtermos informações sobre a seção de choque e da constante de velocidade. Neste trabalho, são desenvolvidos seis capítulos, sendo o primeiro destinado à introdução, e o último, às conclusões. Nos capítulos 2, 3 e 4, é feita uma revisão de literatura, que fornece um embasamento teórico para o estudo realizado. No capítulo 5, descrevemos a metologia utilizada e apresentamos os resultados obtidos. / Energy transfer in molecular collisions are an area of great interest in the scientific field. Because of this, we investigate the vibrational excitation and deactivation process when we study the non-reactive collision between N2 and H2, with 10kcal/mol ≤ Etr ≤ 100kcal/mol, finding computationally vibrational distributions of N2, in order to obtain information about the cross section and the rate constant. In this work, six chapters are developed, the first one is for the introduction, and the last, for the conclusions. In chapters 2, 3 and 4, we present a literature review. In chapter 5, we describe the methodology used and present the results obtained.