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Mesoscopic diffusion as a non-Markov process

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  • Godoy, Salvador
  • Garcı́a-Colı́n, L.S.

Abstract

We use both classical and quantum S-matrix theories to derive expressions for the ballistic diffusion current of a 1D mesoscopic crystalline solid. For both theories, we get the same local Fick’s law, thus proving that local Fick’s law and its associate local diffusion coefficient are incoherent results. The non-local Landauer diffusion coefficient is an incoherent result valid only for solids with a length larger than the coherence length. For solids with a length less than the coherence length, we show that quantum interference gives a new contribution for the non-local diffusion coefficient.

Suggested Citation

  • Godoy, Salvador & Garcı́a-Colı́n, L.S., 1998. "Mesoscopic diffusion as a non-Markov process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 258(3), pages 414-428.
    • Handle: RePEc:eee:phsmap:v:258:y:1998:i:3:p:414-428
    DOI: 10.1016/S0378-4371(98)00217-9
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    Cited by:

    1. Hang Yu & Chenhui Zhu & Lu Yao & Yan Ma & Yang Ni & Shenkai Li & Huan Li & Yang Liu & Yuming Wang, 2023. "The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation," Mathematics, MDPI, vol. 11(5), pages 1-12, February.
    2. Povstenko, Y.Z., 2010. "Evolution of the initial box-signal for time-fractional diffusion–wave equation in a case of different spatial dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4696-4707.

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