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:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“The mere existence of an additional child or children in the family could signify Less. Less time alone with parents. Less attention for hurts and disappointments. Less approval for accomplishments. . . . No wonder children struggle so fiercely to be first or best. No wonder they mobilize all their energy to have more or most. Or better still, all.”
—Adele Faber (20th century)
“I am thankful for small mercies. I compared notes with one of my friends who expects everything of the universe, and is disappointed when anything is less than best, and I found that I begin at the other extreme, expecting nothing, and am always full of thanks for moderate goods.”
—Ralph Waldo Emerson (1803–1882)