Challenges for first-principles methods in theoretical and computational physics: multiple excitations in many-electrons systems and the Aharonov-Bohm effect in carbon nanotubes

Abstract

In the first part of the thesis we will describe double excitations in the absorption spectrum. Double excitations are a peculiar effect of interacting systems which does not have a counterpart in non-interacting ones. The optical absorption spectrum of a system is obtained by shining light on it. At the microscopic level photons hit the electrons which sit in the ground state and change their configuration. If the light source is not too intense this can be described in linear response; that is only "one photon" processes are involved, only one electron per time can be influenced. Here is where the interaction comes in. The hit electron is linked to the others and so other process take place, one of these is the appearance of multiple excitations. In the second part of the thesis we focus on the application of more standard techniques to the description of carbon nanotubes (CNTs). In particular we focus on the effects of magnetic fields on CNTs. CNTs are quasi 1D-systems composed by carbon atoms which have been discovered in 1952. Under the effect of a magnetic field electrons delocalized on a cylindrical surface display a peculiar behaviour, known as Aharonov-Bohm effect. The Aharonov-Bohm is a pure quantum mechanical effect which does not have any counterpart in classical physics. In CNTs the Aharonov-Bohm modify the electronic gap and so can be used to tune the electronic properties. Though a model able to account for such process is available in the literature, in the present work we will describe the effect of magnetic fields "ab-initio". In the description of CNTs we will use standard approximations which are by far much more accurate and general than any approximation introduced in phenomenological descriptions based on model systems.