# Brownian motion

1. Aug 27, 2006

### lokofer

Brownian motion....

Hello ..since it has several application to physics i would like to hear about Brownian motion..in fact i think you can approach it by means of a functional integral of the form:

$$\int D[x] e^{-a \int_{a}^{b} L(x,\dot x, t)}$$ and that from this you derive the "difussion" process... my question is about the trajectories (it'll sound to you familiar to QM if known)

- What's the PDE equation satisfied by the functional integral above?..

- Can the "Brownian motion" by formulated only in probability terms or are there "classical trajectories" that can be obtained?..i heard (wikipedia) about the equation for Brwonian motion in the form:

$$m \ddot x = -\nabla V + \eta (t)$$ where the last extra term was some kind of "random" force applied to the particles.