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Diffusion Processes

  • Chapter
Stochastic Processes

Abstract

Here we discuss diffusion processes as they occur in various areas of physics. We first return to a discussion of random walks, treating the Polya problem and continuous time random walks. Then Brownian motion is analyzed in detail. We discuss the Kramers problem and exemplify the application of statistical and stochastic concepts to physics using the kinetic Ising model. Finally, following E. Nelson, we show how conservative diffusion processes can be described and that this description can be used as a foundation of quantum mechanics from which the Schrödinger equation can be derived. We apply this approach to the tunnel problem and to quantum field theory.

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Notes

  1. 1.

    Time homogeneity means that p(x,t|x 0,0) only depends on the time difference.

  2. 2.

    This is an exercise in van Kampen’s book [101], Chap. XII.

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Authors and Affiliations

  1. Institut für Physik, Martin-Luther-Universität, Halle (Saale), Germany

    Wolfgang Paul

  2. Institut Charles Sadron, Université de Strasbourg, Strasbourg, France

    Jörg Baschnagel

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  1. Wolfgang Paul
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  2. Jörg Baschnagel
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Paul, W., Baschnagel, J. (2013). Diffusion Processes. In: Stochastic Processes. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00327-6_3

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