Cold atoms in low dimensions -- a laboratory for quantum dynamics

Cold atomic gases have become a paradigmatic system for exploring fundamental physics, while at the same time allowing to explore applications in quantum technologies. The accelerating developments in the field have led to a highly advanced set of engineering techniques that, among others, can tune interactions, shape the external geometry, select among a large set of atomic species with different properties, as well as control the number of atoms. In particular, it is possible to operate in lower dimensions and drive atomic systems in the strongly correlated regime. In this review, we discuss recent advances in few-body cold atom systems confined in low dimensions from a theoretical viewpoint. We mainly focus on bosonic systems in one dimension and provide an introduction to the well-known static properties before we discuss the state-of-the-art quantum dynamical processes stimulated by the presence of correlations. Besides describing the fundamental physical phenomena arising in these systems, we also provide an overview of the tools and methods that are commonly used, thus delivering a balanced and comprehensive overview of the field. We conclude by giving an outlook on possible future directions that are interesting to explore in these correlated systems.