When few electrons are tightly confined in a small slice of matter, they tend to occupy well defined positions giving rise to the so called “Wigner molecule”, a strongly correlated electron state of the condensed matter. It is characterized by strong fluctuations of the density and even more by marked peaks of the density-density correlation function, in analogy with conventional solids and molecules.

We employ two different techniques to tackle the study of this system. In planar systems, such as circular quantum dots, we have set-up numerical self-consistent Hartree-Fock methods with embedded symmetry restoration.In one-dimensional systems such as nanowires or carbon nanotubes, we employ analytical techniques such as the Luttinger liquid theory supplemented with the bosonization technique.

Our aim has been to detect how the transition towards the Wigner molecule regime is detectable in electronic transport. In circular dots, we have shown how the linear conductance is markedly suppressed by the formation of these strongly correlated systems. In one-dimensional systems we have shown how the Wigner molecule can be detected by means of STM or charged AFM tips and how thermal effects may even enhance the visibility of the molecule in suitable regimes.