Statistical physics deals with
systems composed of a large number of particles. The state of such
systems is usually described by a distribution function, which allows
us to determine the relevance of a certain configuration and to
calculate macroscopic quantities, as the mean of physical observables.
Gaussian distributions often occur whenever dealing with systems
consisting of a large number of particles. These distributions well
describe dynamics dominated by a large number of small random events,
as for example the erratic motion of a small particle in water
(Brownian motion). Not every system can however be described by
Gaussian distributions, and there are situations in which the dynamics
is dominated by rare and large fluctuations, in striking contrast with
the Brownian motion corresponding to a Gaussian distribution. These
large fluctuations result in long, power-law tail distributions,
commonly termed Levy distributions. Associated to the long tail is the
divergence of the first and/or second moment of these distibutions.
to their tunability, cold atom systems, and more specifically cold
atoms in optical lattices, have proven to be an ideal system to study
the transition from Gaussian distributions and normal diffusion to
power-law tail distributions and anomalous diffusion. In this talk I
will review the workd done with cold atoms and ions in this context,
and discuss possible future development of the field.