Transport phenomena in disordered time-dependent potentials

In this thesis the transport of ultracold atoms trapped in one-dimensional random potentials is investigated from a theoretical and numerical point of view. The randomness of potentials is both in space, i.e. disorder, and time, i.e. noise. The first leads to Anderson localization, while the second tends to destroy it. Moreover we count for interactions among particles, which end up into nonlinear phenomena that destroy the localization or enhance it, but in a differet way with respect to Anderson type, depending on the sign (i.e. repuslive or attractive). First chapter deals with the interpretation of Anderson localization. The second with the interplay between disroder, noise and interactions, giveing a portrait of the possible scenarios coming from their different combination. We built a model which describes the diffusion in certain regime, which are in good agreement with the experimental data coming from recent works done in Florence, at LENS. In the third and last chapter we consider two interacting condensates in the case that one creates a disordered potentential felt by the other. In such a way we create an atomic trapping potential onto which the second species moves, and we study its dynamics.