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Pereira, Eduardo Jorge Nunes

Universidade do Minho: RepositoriUM

Stochastic models of anomalous diffusion in incoherent radiation trappingEduardo J. Nunes-PereiraUniversidade do Minho, Escola de Cieˆncias,Departamento de F´ısica, 4710-057 Braga, Portugal.epereira@fisica.uminho.pt(Dated: February 29, 2008)This contribution is divided into four parts. In the first part the problem of incoherent reso-nance radiation trapping is defined, briefly stating both its fundamental character of a transportprocess as well as its main practical applications (discharge processes in gases, plasma and atomicvapour luminescence, electric discharge and electrodeless fluorescence lamps, plasma display panels,radiation transfer in stellar atmospheres, etc.). Radiation trapping is also known as imprisonmentof resonance radiation, reabsorption, self-absorption, line transfer, radiation diffusion or multiplescattering of resonance radiation.The second part constitutes the main focus of the talk. In it, the photonic superdiffusive motion isdiscussed making use of both the jump length and the single line opacity distribution functions (bothdefined from the single line spectral distribution). General expressions are given which relate theasymptotic behaviour of the three interconnected distribution functions. The problem of completefrequency redistribution for Doppler, Lorentz and Voigt line shapes is first addressed. Photonictrajectories are shown to be well characterized Le´vy flights displaying characteristic long tails (su-perdiffusive transport properties). It is shown that the asymptotic form is a strict power-law r−3/2for Lorentz, while for Doppler the asymptotic is r−2 (ln r)−1/2, where r stands for the jump length.For the Voigt profile, the asymptotic form has always a Lorentz character, but the trajectory isa self-affine fractal with two characteristic Hausdorff scaling exponents. Some interesting but inthis context marginal facts are briefly mentioned (incoherent transport is always superdiffusive ir-respective of the spectral distribution, the asymptotic for a unidimensional formulation of radiationtransfer, the one used in the standard plane-parallel stellar atmosphere problem, is the same asthe asymptotic of the usual jump size distribution and that the deduced power-law asymptotics areindeed expected to hold in a large number of practical situations). The line opacity distributionfunction is then generalized for partial frequency redistribution (PFR) conditions and several possi-ble redistribution mechanisms (pure Doppler broadening, combined natural and Doppler broadeningand combined Doppler, natural and collisional broadening) discussed. With partial redistribution,there are two coexisting scales with a different behavior: the small scale is controlled by the in-tricate PFR details while the large scale is essentially given by the atom rest frame redistributionasymptotic. The pure Doppler and combined natural, Doppler and collisional broadening are charac-terized by both small and large scale superdiffusive Le´vy flight behaviors while the combined naturaland Doppler case has an anomalous small scale behavior but a diffusive large scale asymptotic. Theconditions for the breakdown of superdiffusion in combined natural and Doppler broadening aredefined.Finally, in the last two parts the previous work is briefly put into perspective in a broader context.In the third part some stochastic models to quantify the dynamics of radiation trapping are presentedgiving particular emphasis to the actual experimentally accessible observables and the the conditionsin which the previous presented asymptotics are expected to dominate the overall behaviour of realsystems. In the last fourth part, the recent reevaluation of the importance of anomalous diffusionfor radiation transport is put into historical perspective by comparing recent results with importantseminal contributions dated from the 1930s (breakdown of standard diffusion), 1940s (the well-known Holstein-Biberman equation), and 1980s (breakdown of superdiffusion in some conditions forpartial redistribution).[1] M. N. Berberan-Santos, E. Pereira, and J. M. G. Martinho, Dynamics of Radiative Transport, in Resonance Energy Transfer,edited by D. L. Andrews and A. A. Demidov (John Wiley & Sons, Chichester, 1999).[2] E. Pereira, J. M. G. Martinho, and M. N. Berberan-Santos, Phys. Rev. Lett. 93, 120201 (2004).[3] M. N. Berberan-Santos, E. J. Nunes-Pereira, and J. M. G. Martinho, J. Chem. Phys. 125, 174308 (2006).[4] A. R. Alves-Pereira, E. J. Nunes-Pereira, J. M. G. Martinho, and M. N. Berberan-Santos, J. Chem. Phys. 126, 154505(2007).[5] A. R. Alves-Pereira, E. J. Nunes-Pereira, J. M. G. Martinho, and M. N. Berberan-Santos, Eur. J. Phys. 28, 1105 (2007).

Stochastic models of anomalous diﬀusion in incoherent radiation trapping

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Stochastic models of anomalous diﬀusion in incoherent radiation trapping

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Universidade do Minho: RepositoriUM