# Mathias Albert - Institut de Physique de Nice - Keywords: symmetry, quantum gases, one dimensional systems

Indistinguishable particles are generally classified in two families: the so called bosons and fermions. At the microscopic level, this means that their wave function is either symmetric or anti-symmetric with respect to permutation of particles which has extremely important consequences at the macroscopic level. Indeed, from such simple rules may emerge spectacular phenomena like super-conductivity or quantum pressure responsible for the stability of neutron star for instance.

When particles leave in a one dimensional world, and are subjected to strong interactions, the situation is much richer and mixture of particles may exhibits more exotic symmetries. Such mixtures are now extremely well controlled in cold atoms experiments and are a new laboratory for studying theoretical physics and its applications beyond the zoo of standard elementary particles.

In this contribution, we will give an overview of the last theoretical progresses in this field and how it is connected to real experiments and other fields like quantum magnetism for instance. We will in particular discuss how to relate abstract theoretical concepts like symmetry over permutation to simple and experimentally observable quantities like the Tan's contact which is measurable in the velocity distribution of an assembly of particles.