Quantum transport in chaotic/complex systems

• Grant number: 08/02852-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2008
• End date: August 31, 2009
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: Marcus Aloizio Martinez de Aguiar
• Grantee: Marcel Novaes
• Host Institution: Instituto de Física Gleb Wataghin (IFGW). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This main aim of this project is to further develop the theoretical approaches to electronic transport in quantum dots. The typical experimental conditions have two very important characteristics: 1) interferences effects are important, due to the long coherence time; 2) geometries in which the classical dynamics is chaotic. We will consider two types of descriptions for these systems. The first one is purely phenomenological and consists in replacing quantum operators by random matrices. The second one is microscopic and is based on the semiclassical approximation. Both theories work well in the perturbative regime, in which the systems conductance is large. Non-perturbative results, on the other hand, are rare. This situation is not satisfactory, since many experiments are done at low conductance. We shall extend and complement both theories in order to be able to obtain non-perturbative results in a systematic way. A second objective is to treat quantum transport in fractal structures in two and three dimensions. Although with a smaller potential for practical applications, this topic is very interesting because it is a feasible model for problems with high geometrical complexity.