Book ChapterDOI
Fokker-Planck Equation
Hannes Risken
- pp 63-95
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TLDR
In this paper, an equation for the distribution function describing Brownian motion was first derived by Fokker [11] and Planck [12] and it is shown that expectation values for nonlinear Langevin equations (367, 110) are much more difficult to obtain.Abstract:
As shown in Sects 31, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (31, 31) For nonlinear Langevin equations (367, 110) expectation values are much more difficult to obtain, so here we first try to derive an equation for the distribution function As mentioned already in the introduction, a differential equation for the distribution function describing Brownian motion was first derived by Fokker [11] and Planck [12]: many review articles and books on the Fokker-Planck equation now exist [15 – 15]read more
Citations
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Journal ArticleDOI
Fokker–planck-based control of a two-level open quantum system
Mario Annunziato,Alfio Borzì +1 more
TL;DR: In this paper, the authors considered the control of a two-level open quantum system subject to dissipation due to environment interaction and proposed a Fokker-Planck control framework.
Journal ArticleDOI
HJB and Fokker-Planck equations for river environmental management based on stochastic impulse control with discrete and random observation
TL;DR: A new two-variable river environmental restoration problem based on jump stochastic differential equations (SDEs) governing the sediment storage and nuisance benthic algae population dynamics in a dam-downstream river is formulated and it is demonstrated that simple numerical schemes can handle these equations.
Journal ArticleDOI
Modeling Maximum Entropy and Mean-Field Interaction in Macroeconomics
TL;DR: In this paper, the authors propose a stochastic dynamic model with heterogeneous firms, in which the responses of firms to stochastically perturbed events modifies their financial ratios, determining the evolution of the system.
Journal ArticleDOI
Diffusion Coefficient of a Brownian Particle in Equilibrium and Nonequilibrium: Einstein Model and Beyond
TL;DR: In this article , the temperature dependence of the diffusion coefficient of a Brownian particle is studied in the context of Langevin dynamics, and it is shown that the coefficient exhibits an intriguingly non-monotonic dependence on temperature.
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Path sampling for collapse rates of metastable magnetic skyrmions and direct comparison with transition state theory
TL;DR: In this article, a comparison between transition state theory and forward flux sampling is performed to compute collapse rates of metastable magnetic skyrmions, and a good agreement is obtained between the two methods.
References
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Journal ArticleDOI
Fluctuations and Irreversible Processes
Lars Onsager,S. Machlup +1 more
TL;DR: In this paper, the probability of a given succession of (nonequilibrium) states of a spontaneously fluctuating thermodynamic system is calculated, on the assumption that the macroscopic variables defining a state are Gaussian random variables whose average behavior is given by the laws governing irreversible processes.
Journal ArticleDOI
The Radiation Theories of Tomonaga, Schwinger, and Feynman
TL;DR: In this article, a unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory.
Journal ArticleDOI
Covariant formulation of non-equilibrium statistical thermodynamics
TL;DR: In this paper, the diffusion matrix of the Fokker Planck equation is used as a contravariant metric tensor in phase space, and the covariance of the Langevin-equations and the fokker equation is demonstrated.
Journal ArticleDOI
Approximation of the Linear Boltzmann Equation by the Fokker-Planck Equation
TL;DR: In this article, the first two terms of the Kramers-Moyal expansion of the Fokker-Planck equation were used to approximate the linear Boltzmann integral operator.