  One-dimensional systems of interacting atoms are an ideal laboratory to study
the Kosterlitz-Thouless phase transition. In the renormalization group picture
there is essentially a two-parameter phase diagram to explore. We first present
how detailed experiments have shown direct evidence for the theoretical
treatment of this transition. Then generalization to the case of two-component
systems with bound state formation is discussed. Trimer formation in the
asymmetric attractive Hubbard model involve in a crucial way this kind of
physics.
