Abstract
We asymptotically derive a non-linear Langevin-like equation with non-Gaussian white noise for a wide class of stochastic systems associated with multiple stochastic environments, by developing the expansion method in our previous paper (Kanazawa et al. in Phys Rev Lett 114:090601–090606, 2015). We further obtain a full-order asymptotic formula of the steady distribution function in terms of a large friction coefficient for a non-Gaussian Langevin equation with an arbitrary non-linear frictional force. The first-order truncation of our formula leads to the independent-kick model and the higher-order correction terms directly correspond to the multiple-kicks effect during relaxation. We introduce a diagrammatic representation to illustrate the physical meaning of the high-order correction terms. As a demonstration, we apply our formula to a granular motor under Coulombic friction and get good agreement with our numerical simulations.
Original language | English |
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Pages (from-to) | 1294-1335 |
Number of pages | 42 |
Journal | Journal of Statistical Physics |
Volume | 160 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2015 Sep 1 |
Externally published | Yes |
Keywords
- Granular motor
- Langevin equation
- Non-Gaussian noise
- Non-linear friction
- Stochastic processes
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics