Since the invention of the transistor in 1947 and the development of integrated circuits in the late 1950’s, there was a rapid progress in the development and miniaturization of the solid state devices and electronic circuit components. This miniaturization raises a question “How small do we have to make a device in order to get fundamentally new properties?” [1], or more concretely, when do the quantum effects become important. During the last 30 years, the innovations in fabrication and cooling techniques allowed to produce nanometer scale solid-state or single molecule-based devices and to perform electrical transport experiments at temperatures below one Kelvin (1 K), and thus to address such question. In this thesis we are concerned with the theoretical description of one kind of such devices called quantum dots.

As the name suggest a quantum dot is a system where particles are confined in all three directions, which makes it effectively zero dimensional and corresponds to discrete electronic orbitals (levels) and excitation spectrum. This is analogous to the situation in atoms, where confinement potential replaces the potential of the nucleus, thus quantum dots are often referred to as artificial atoms [2, 3]. Additionally, in order for the system to be truly quantum, the size of the dot has to be comparable to the de Broglie wavelength of the electrons in it. What we have mentioned so far is rather abstract conditions, which practically can be realized in various systems, such as, electrically confined electrons in semiconductor nanowires, two dimensional electron gases, carbon nanotubes, or just small metallic particles, nanoscale pieces of semiconductor.