Continuous Time Random Walk (CTRW) put to work

  • Harvey Scher
Regular Article
Part of the following topical collections:
  1. Topical issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook


A personal history of the first applications of CTRW to the physics of transport and diffusion in disordered media is presented. The sequence of steps leading to the introduction of novel ψ(t), the probability density of particle-transfer times, without moments is briefly outlined. The key concept that emerged from those early applications is anomalous or non-Fickian transport. The latter involved spatial moments of the particle propagator with completely different time behavior, e.g., the mean <l> ∝ t β , 0 < β < 1 and likewise σ the rms spreading, i.e., <l>∕σ = constant. With these results many puzzling experimental data were explained. The data ranged from electronic dynamics of amorphous films to chemical migration and interaction in the subsurface of the Earth. These were not anticipated results but a consequence of the CTRW with these special ψ(t).


  1. 1.
    H. Scher, M. Lax, Phys. Rev. B7, 4491 (1973) ADSCrossRefGoogle Scholar
  2. 2.
    E.W. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965) ADSCrossRefGoogle Scholar
  3. 3.
    R. Ben-Zvi, A. Nissan, H. Scher, B. Berkowitz, Eur. Phys. J. B, DOI:  10.1140/epjb/e2017-80417-8
  4. 4.
    D.G. Thomas, J.J. Hopfield, W.M. Augustyniak, Phys. Rev. 140, A202 (1965) ADSCrossRefGoogle Scholar
  5. 5.
    H. Scher, M. Lax, Phys. Rev. B7, 4502 (1973) ADSCrossRefGoogle Scholar
  6. 6.
    E.W. Montroll, H. Scher, J. Stat. Phys. 9, 101 (1973) ADSCrossRefGoogle Scholar
  7. 7.
    H. Scher, E.W. Montroll, Phys. Rev. B12, 2455 (1975) ADSCrossRefGoogle Scholar
  8. 8.
    M.F. Shlesinger, J. Stat. Phys. 10, 421 (1974) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Earth and Planetary SciencesWeizmann Institute of ScienceRehovotIsrael

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