Abstract:
This seminar aims to give an introduction to the physics of strongly
correlated fermions and bosons in one-dimension.
I will start from the description of the Tomonaga-Luttinger-Liquid (TLL)
which has been the cornerstone of our understanding of the properties of
one dimensional systems. This universal set of properties plays in one
dimension, the same role than Fermi liquid plays for the higher
dimensional metals. I will give an overview of some of the experimental
tests that were made to probe such TLL physics. In particular I will
detail some of the recent experiments that were made in spin systems and
which provided remarkable quantitative tests of the TLL physics. Than I
will focus on bosons in one-dimension and  discuss their properties and
the effects of various perturbations on the Tomonaga-Luttinger liquid
state, as well as extensions to multicomponent and out of equilibrium
situations.
These extensions are specially targeted for the experimental realizations
that have been provided by cold atomic gases in optical lattices.