Analytically solvable model in fractional kinetic theory

Robson, R.E., and Blumen, A. (2005) Analytically solvable model in fractional kinetic theory. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 71 (6). 061104.

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In this article we give a general prescription for incorporating memory effects in phase space kinetic equation, and consider in particular the generalized “fractional” relaxation time model equation. We solve this for small-signal charge carriers undergoing scattering, trapping, and detrapping in a time-of-flight experimental arrangement in two ways: (i) approximately via the Chapman-Enskog scheme for the weak gradient, hydrodynamic regime, from which the fractional form of Fick’s law and diffusion equation follow; and (ii) exactly, without any limitations on gradients. The latter yields complete and exact expressions in terms of generalized Mittag-Lefler functions for experimentally observable quantities. These expressions enable us to examine in detail the transition from the nonhydrodynamic stage to the hydrodynamic regime, and thereby establish the limits of validity of Fick’s law and the corresponding fractional diffusion equation.

Item ID: 9641
Item Type: Article (Research - C1)
ISSN: 1550-2376
Date Deposited: 24 Mar 2010 22:30
FoR Codes: 02 PHYSICAL SCIENCES > 0204 Condensed Matter Physics > 020405 Soft Condensed Matter @ 100%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970102 Expanding Knowledge in the Physical Sciences @ 100%
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