Statistical Mechanics for Athermal Fluctuation by Kiyoshi Kanazawa

Author:Kiyoshi Kanazawa
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

8.2.2 Derivation of Non-Gaussian Langevin Equations Under Nonlinear Frictions

We then derive non-Gaussian Langevin equations with nonlinear friction terms. Nonlinear frictions are ubiquitous in nature [12–14] and are known to appear in systems such as granular [15–17], biological [18–20] and atomic-surface ones [21–23]. We note that nonlinear frictions can be discontinuous functions with respect to velocity in general (e.g., Coulombic friction), and their singular effects on stochastic properties have been interesting topics [1–4, 7, 8, 24–32]. Indeed, as will be shown in the next section, the distribution function can be strongly singular around the peak. We here introduce critical assumptions as follows: (NL1) Small noise assumption: The noise amplitudes in and are small. In other words, their stochastic parts are scaled by a small positive constant as

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