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:
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“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)
“In trying to understand the appeal of best-sellers, it is well to remember that whistles can be made sounding certain notes which are clearly audible to dogs and other of the lower animals, though man is incapable of hearing them.”
—Rebecca West (1892–1983)