Bisquert J. Fractional diffusion in the multiple-trapping regime and revision of the equivalence with the continuous-time random walk.
PHYSICAL REVIEW LETTERS 2003;
91:010602. [PMID:
12906528 DOI:
10.1103/physrevlett.91.010602]
[Citation(s) in RCA: 45] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2002] [Indexed: 05/24/2023]
Abstract
We investigate the macroscopic diffusion of carriers in the multiple-trapping (MT) regime, in relation with electron transport in nanoscaled heterogeneous systems, and we describe the differences, as well as the similarities, between MT and the continuous-time random walk (CTRW). Diffusion of free carriers in MT can be expressed as a generalized continuity equation based on fractional time derivatives, while the CTRW model for diffusive transport generalizes the constitutive equation for the carrier flux.
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