Lecturer: Prof. David Kessler
Affiliation: Bar-Ilan University
Abstract:
Lévy flights are a form of random walk
where the jump distances are power-law
distributed. The distribution function of
the position after N jumps is given,
according to the Generalized Central Limit
Theorem, by a Lévy \alpha-stable
distribution, with a power-law tail. The
moments of such a distribution are infinite.
To correct this problem, Blumen, Klafter
and Zumofen invented the concept of a
Lévy walk, which is a Lévy flight where
the time of the flight increases with the
distance traveled, so a particle cannot go
an infinite distance in a finite time.
However, till now, there has been no
physical system which one could show
from first principles that it executed such a
Lévy walk. We show how cold atoms
undergoing Sisyphus cooling in an atomic
trap should indeed do a Lévy walk, and
derive the properties thereof. We discuss
the experimental status of this system,
which does not yet yield results in
agreement with the theory.