Photonic superdiffusive motion in resonance radiation trapping

Abstract

In this work we consider the relation between the jump length probability density function and the line shape function in resonance radiation trapping in atomic vapors. The two-sided jump length probability density function suitable for a unidimensional formulation of radiative transfer is also derived. As a side result, a procedure to obtain the Maxwell distribution of velocities from the Maxwell-Boltzmann distribution of speeds was obtained. General relations that give the asymptotic jump length behavior and the Levy flight parameter mu for any line shape are obtained. The results are applied to generalized Doppler, generalized Lorentz, and Voigt line shape functions. It is concluded that the lighter the tail of the line shape function, the less heavy the tail of the jump length probability density function, although this tail is always heavy, with mu < or =1.