Path Integral Formulation of Anomalous Diffusion Processes

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Friedrich, Rudolf ; Eule, Stephan (2011)
  • Subject: Condensed Matter - Statistical Mechanics

We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of processes under consideration. We show that Continuous Time Random Walks (CTRWs) are included in our framework. A closed expression for the path probability distribution of CTRWs is found in terms of their waiting time distribution as the solution of a Dyson equation. As the formalism naturally includes the treatment of functionals a generalized Feynman-Kac formula is derived.
  • References (18)
    18 references, page 1 of 2

    [1] F. Langouche, D. Roekaerts and E. Tirapegui, Functional Integration and Semiclassical Expansions (Reidel, Dordrecht, The Netherlands, 1982).

    [2] H. Kleinert Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets (World Scientific, Singapore, 2009).

    [3] L. Onsager and S. Machlup, Phys. Rev. 91, 1505 (1953).

    [4] H. Haken, Z. Phys. B 24, 321 (1976); R. Graham, Z. Phys. B 26, 281 (1977); P. H¨anggi Z. Physik B 75, 275 (1989).

    [5] J.P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990).

    [6] R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000); R. Metzler and J. Klafter, J. Phys. A:Math. Gen. 37, R161 (2004).

    [7] M.F. Shlesinger, G.M. Zaslavsky and J. Klafter, Nature 363, 31 (1993).

    [8] E. Montroll and G.H. Weiss, J. Math. Phys 6, 167 (1965).

    [9] H.C. Fogedby, Phys. Rev. E 50, 1657 (1994); S. Eule and R. Friedrich, EPL 86, 30008 (2009).

    [10] A. Baule and R. Friedrich, Phys. Rev. E 71, 026101 (2005).

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