Interactions in quasicrystals

Although the effects of interactions in solid state systems still remains a widely open subject, some limiting cases such as the three dimensional Fer mi liquid or the one-dimensional Luttinger liquid are by now well understoo d when one is dealing with interacting electrons in periodic crystalline st ructures. This problem is much more fascinating when periodicity is lacking as it is the case in quasicrystalline structures. Here, we discuss the inf luence of the interactions in quasicrystals and show, on a controlled one-d imensional model, that they lead to anomalous transport properties, interme diate between those of an interacting electron gas in a periodic and in a d isordered potential.