Photonic superdiffusive motion in resonance line radiation trapping - partial frequency redistribution effects

The relation between the jump length probability distribution function and the spectral line profile in resonance atomic radiation trapping is considered for Partial Frequency Redistribution (PFR) between absorbed and reemitted radiation. The single line Opacity Distribution Function [M.N. Berberan-Santos et.al. J.Chem.Phys. 125, 174308 (2006)] is generalized for PFR and used to discuss several possible redistribution mechanisms (pure Doppler broadening, combined natural and Doppler broadening and combined Doppler, natural and collisional broadening). It is shown that there are two coexisting scales with a different behavior: the small scale is controlled by the intricate PFR details while the large scale is essentially given by the atom rest frame redistribution asymptotic. The pure Doppler and combined natural, Doppler and collisional broadening are characterized by both small and large scale superdiffusive Levy flight behaviors while the combined natural and Doppler case has an anomalous small scale behavior but a diffusive large scale asymptotic. The common practice of assuming complete redistribution in core radiation and frequency coherence in the wings of the spectral distribution is incompatible with the breakdown of superdiffusion in combined natural and Doppler broadening conditions

Photon trajectories in incoherent atomic radiation trapping as Levy flights

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 always has a Lorentz character, but the trajectory is a self-affine fractal with two characteristic Hausdorff scaling exponents