Talk:Langevin equation

To do
To do: -Add a section (or a new page? or both with one a summary of the other?) on noise terms, explaining what is meant by a 'continuous random function', what is needed to specify it (correlation functions) (i.e. the systems described on the page are not completely specified).

-More examples of Langevin equations (e.g.from lasers, chemical kinetics, population dynamics etc.)

-Tidy up inline maths (...help on this would be good...)

SgtThroat 11:37, 27 Aug 2004 (UTC)

Having looked around I've realised that the term Langevin equation is more specific than just an SDE in physics, although it is sometimes used in that way. Thus I've moved some of the more general info I added a while back to a new article stochastic differential equations, as I feel that the two things warrant seperation. --SgtThroat 14:50, 4 Jan 2005 (UTC)

Another form
Another form of the Langevin used in Statistical mechanics ignores inertial accelerations like ma, and instead approximate the velocity of the suspended particles as having a velocity that is linearly related to the forces acting upon the particle. This is in the small particle limit, so $$m \frac{d^2x}{dt^2}$$ is negligible in comparision to the other terms. Consequently, the form of "the" Langevin equation I am used to using is

$$\zeta \frac{d \mathbf{x}}{dt} = \frac{\partial \mathbf {V}}{\partial x} + \mathbf {f} \left (t \right)$$ where the f(t) term is the stochastic variable and $$\frac{1}{\zeta}$$ is known as the "mobility" of the particle in a viscous fluid. Whilst this would be a minor edit to the page, I think it is a valid one to mention this small particle limit. --Lateralis 22:32, 16 January 2006 (UTC)

Variables clarification
Can we add a clarification to what the variables mean? I know what m, ma, d, dv and F are, but the majority of people looking this up on Wikipedia are probably doing so because they are unfamiliar with Physics. I am still working on figuring out B and n(t) —Preceding unsigned comment added by Bvbellomo (talk • contribs) 13:49, 16 November 2007 (UTC)

Langevin dynamics
I added a link to the Wiener process page for the noise term. Also, this article really should be combined with the Langevin dynamics page. Nonfcomm (talk) 21:51, 25 March 2009 (UTC)
 * There is a very short merge discussion on the talk page there. At Talk:Langevin dynamics. 67.198.37.16 (talk) 23:47, 23 May 2024 (UTC)

Non-linear ref
Is the following information relevant to the part on solving (non-linear) Langevin Equations & can appropriate text be put in by someone qualified to do so? It is from a citation for Prof W.T.Coffey (author of cited books on The Langevin Equation) when he became a Fellow of the American Physical Society in 1999: "Coffey, William Thomas [1999] Trinity College Dublin. Citation: For development of new methods for the solution of the nonlinear Langevin equation without the use of the Fokker-Planck equation, allowing the exact calculation of correlation times and mean first passage times." 15:07, 16 June 2010‎ User:193.113.57.161

Index?
I'm having difficulty understanding the meaning of these equations because theres no mention here (or anywhere that i can find so far on the internet) as to what the index is referring to within the equations. Is it as simple as coordinates? or a more complicated set of operators? — Preceding unsigned comment added by 143.167.5.177 (talk) 13:48, 30 March 2012 (UTC)

Recovering Boltzmann Statistic
This section should use the same conventions as other sections: $$\lambda$$ for the damping coefficient and $$\eta$$ for the fluctating force. After all it should be article and not a collection of sections. radical_in_all_things (talk) 09:26, 23 April 2016 (UTC)


 * It appears that this was fixed, at some point in the past. 67.198.37.16 (talk) 22:15, 23 May 2024 (UTC)