Photon trajectories in incoherent atomic radiation trapping as Levy flights

Abstract

Photon trajectories in incoherent radiation trapping for Doppler, Lorentz and Voigt line shapes under complete frequency redistribution are shown to be Levy flights. The jump length (r) distributions display characteristic long tails. For the Lorentz line shape, the asymptotic form is a strict power-law r^{-3/2} while for Doppler the asymptotic is r^{-2} (ln r)^{-1/2}. For the Voigt profile, the asymptotic form has always a Lorentz character, but the trajectory is a self-affine fractal with two characteristic Hausdorff scaling exponents.