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)
“The world will never be long without some good reason to hate the unhappy; their real faults are immediately detected, and if those are not sufficient to sink them into infamy, an additional weight of calumny will be superadded.”
—Samuel Johnson (1709–1784)
“If the heart of a man is deprest with cares,
The mist is dispell’d when a woman appears;
Like the notes of a fiddle, she sweetly, sweetly
Raises the spirits, and charms our ears.”
—John Gay (1685–1732)