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In the first part of the thesis we will describe double excitations in theabsorption spectrum. Double excitations are a peculiar effect of interactingsystems which does not have a counterpart in non-interacting ones. The opticalabsorption spectrum of a system is obtained by shining light on it. At themicroscopic level photons hit the electrons which sit in the ground state andchange their configuration. If the light source is not too intense this can bedescribed in linear response; that is only "one photon" processes are involved,only one electron per time can be influenced. Here is where the interactioncomes in. The hit electron is linked to the others and so other process takeplace, one of these is the appearance of multiple excitations.  In the second part of the thesis we focus on the application of more standardtechniques to the description of carbon nanotubes (CNTs). In particular wefocus on the effects of magnetic fields on CNTs. CNTs are quasi 1D-systemscomposed by carbon atoms which have been discovered in 1952. Under the effectof a magnetic field electrons delocalized on a cylindrical surface display apeculiar behaviour, known as Aharonov-Bohm effect. The Aharonov-Bohm is a purequantum mechanical effect which does not have any counterpart in classicalphysics. In CNTs the Aharonov-Bohm modify the electronic gap and so can be usedto tune the electronic properties. Though a model able to account for suchprocess is available in the literature, in the present work we will describethe effect of magnetic fields "ab-initio". In the description of CNTs we willuse standard approximations which are by far much more accurate and generalthan any approximation introduced in phenomenological descriptions based onmodel systems.

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