Langevin equations

The generalised Langevin equation can be considered as a mathematical rearrangement of the Liouville's theorem.

${\frac {da(t)}{dt}}=i\Omega a(t)-\int _{0}^{t}K(s)a(t-s)+F(t)~{\mathrm {d} }t$

where $a(t)$ is a set of dynamical variables, $K(s)$ is a damping function and $\Omega$ is a frequency matrix.

See also

• Brownian motion

References

1. Hazime Mori "Transport, Collective Motion, and Brownian Motion", Progress of Theoretical Physics 33 pp. 423-455 (1965)