Other Examples and Additional Notes
A solution of a Langevin equation for a particular realization of the fluctuating force is of no interest by itself, what is of interest are correlation functions of the slow variables after averaging over the fluctuating force.
One method of solution makes use of the Fokker–Planck equation, which provides a deterministic equation satisfied by the time dependent probability density. Alternatively numerical solutions can be obtained by Monte Carlo simulation. Other techniques, such as path integrals have also been used, drawing on the analogy between statistical physics and quantum mechanics (the Fokker-Planck equation is formally equivalent to the Schrödinger equation).
Read more about this topic: Langevin Equation
Famous quotes containing the words examples, additional and/or notes:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“Don’t you think I’ve had enough excitement for one evening, without the additional thrill of a strange man making love to me?”
—John L. Balderston (1899–1954)
“The night is itself sleep
And what goes on in it, the naming of the wind,
Our notes to each other, always repeated, always the same.”
—John Ashbery (b. 1927)