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Path integrals for Fokker-Planck equation described by generalized random walks

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Zeitschrift für Physik B Condensed Matter

Abstract

Path integral representations for Fokker-Planck (FP) equations, described by the random walks (RW) and the generalized random walks (GRW), are given. The GRW is a generalized one from the usual random walks to study non-linear, non-equilibrium processes. The GRW includes some memory effects and couplings through the jumping probabilities. To derive the path integrals of the processes, a transformation of probability, scalings of site (space) and step (time) are performed on the GRW. By a function in the exponent of the path integrals for the FP equation obtained by the RW or the GRW, a “Lagrangian” giving most probable path is introduced. From the Lagrangian, an “effective Hamiltonian” is deduced.

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Authors and Affiliations

  1. Department of Applied Science, Faculty of Engineering, Tohoku University, 980, Sendai, Japan

    Hiroaki Hara

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  1. Hiroaki Hara
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Hara, H. Path integrals for Fokker-Planck equation described by generalized random walks. Z. Physik B - Condensed Matter 45, 159–166 (1981). https://doi.org/10.1007/BF01293330

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  • DOI: https://doi.org/10.1007/BF01293330

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