Coherence properties of strongly interacting quantum mixtures in one dimension
Indiscernability of identical particles has strong consequences in quantum systems. It is for instance responsible for Bose-Einstein condensation or the Pauli exclusion principle through the only fact that the many-body wave function has to be symmetric or anti-symmetric with respect to exchanges of coordinates. In this talk, I will discuss various properties of strongly interacting mixtures of bosons and fermions in one dimension. In particular, I will discuss the symmetry spectroscopy of mixtures with or without SU(N) symmetry. I will also review some recent results on the statistical properties of the momentum occupation numbers in a Tonks-Girardeau gas.