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Communication: A scaling approach to anomalous diffusion
4. N. van Kampen, Stochastic Processes in Physics and Chemistry, revised ed. (North Holland, Amsterdam, 1992),
11. H. Risken, The Fokker-Planck Equation, Springer Series in Synergetics, 2nd ed. (Springer, Berlin, Heidelberg, New York, 1996),
12. K. Oldham and J. Spanier, The Fractional Calculus (Academic Press, New York, London, 1974).
13. NIST Handbook of Mathematical Functions, edited by F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark (Cambridge University Press, 2010).
14. J. Boon and S. Yip, Molecular Hydrodynamics (McGraw Hill, New York, 1980).
15. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Higher Transcendental Functions (McGraw Hill, New York, 1955).
16. A. Kilbas, H. Srivastava, and J. Trujillo, Theory and Applications of Fractional Differential Equations, North Holland Mathematics Studies Vol. 204 (Elsevier, 2006).
17. P. Langevin and C. Rendus, Acad. Sci. Paris 146, 530 (1908).
24. R. Zwanzig, Statistical Mechanics of Irreversibility, Lectures in Theoretical Physics (Wiley-Interscience, New York, 1961), pp. 106–141.
25. R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University Press, 2001).
26. J.-P. Hansen and I. McDonald, Theory of Simple Liquids, 2nd ed. (Academic Press, 1986).
27. J. Karamata, J. Reine Angew. Math. 1931, 27 (1931).
29. Mathematica 9, Wolfram Research Inc., Champaign, Illinois, USA, 2012.
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The paper presents a rigorous derivation of the velocity autocorrelation function for an anomalously diffusing slow solute particle in a bath of fast solvent molecules. The result is obtained within the framework of the generalized Langevin equation and uses only scaling arguments and identities which are based on asymptotic analysis. It agrees with the velocity autocorrelation function of an anomalously diffusing Rayleigh particle whose dynamics is described by a fractional Ornstein-Uhlenbeck process in velocity space. A simple semi-analytical example illustrates under which conditions the latter model is appropriate.
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