Carl McBride: New page: {{stub-general}} The generalised '''Langevin equation''' can be considered as a mathematical rearrangement of the Liouville's theorem. : $\frac{da(t)}{dt}= i\Omega a(t) - \int_0^...$

2008-01-29T13:24:52Z

New page: {{stub-general}} The generalised '''Langevin equation''' can be considered as a mathematical rearrangement of the Liouville's theorem. :<math>\frac{da(t)}{dt}= i\Omega a(t) - \int_0^...

New page

{{stub-general}}
The generalised '''Langevin equation''' can be considered as a mathematical rearrangement of the
[[Liouville's theorem]].

:<math>\frac{da(t)}{dt}= i\Omega a(t) - \int_0^t K(s) a(t-s) + F(t) ~ {\mathrm {d}}t</math>

where <math>a(t)</math> is a set of dynamical variables, <math>K(s)</math> is a damping function and <math>\Omega</math> is a frequency matrix.
==See also==
*[[Brownian motion]]
==References==
#[http://dx.doi.org/10.1143/PTP.33.423 Hazime Mori "Transport, Collective Motion, and Brownian Motion", Progress of Theoretical Physics '''33''' pp. 423-455 (1965)]
[[category: Non-equilibrium thermodynamics]]

Langevin equations - Revision history

Carl McBride: New page: {{stub-general}} 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^...

Carl McBride: New page: {{stub-general}} The generalised '''Langevin equation''' can be considered as a mathematical rearrangement of the Liouville's theorem. : $\frac{da(t)}{dt}= i\Omega a(t) - \int_0^...$