L’evy walks with applications to cold atoms and population biology

L’evy walks with applications to cold atoms and population biology

David Kessler

1) Introduction to The Cold Atom System & Sisyphus Cooling
2) The Fokker-Planck Eqn. for the Momentum Distribution
a) Simulation Approaches: Langevin, Numerical Integration
b) Steady-State Solution and its Sicknesses
c) Long-time scaling solution
3) The Position-Space Distribution
a) Simulation Approaches: Langevin, Master Equation
b) Mapping to Levy walks
c) Discussion of Levy flights/walks
d) The Airy and Bessel Distributions
e) The Infinite-Covariant Density
4) The Luria-Delbruck Problem
a) Introduction to the Problem
b) The Delbruck Approach
c) Picking the Correct Ensemble
d) The Master Equation
e) The Long-Time Solution