# I How to understand diffusive and ballistic transport?

1. Nov 18, 2016

### KFC

Hi there,
I am always confusing in the difference between diffusive and ballistic transport. My understanding on the diffusive transport is from it's name, particles diffuse from the high density region into the low density region. I think the diffusion happens towards all direction, is it why usually it is formulated as $\langle x^2(t) \rangle = Dt$ ? For the ballistic transport, it is very confusing where is the term ballistic from. But my understanding is the transport is linear, is that correct?

I saw that in some article, there mentions transport in momentum. It looks like that the ballistic transport corresponding to quadratic growth of kinetic energy. I don't understand why but if that's the case, how does it look like for energy for diffusive transport in momentum?

Last edited: Nov 18, 2016
2. Nov 18, 2016

### f95toli

I think you need to put your question into some sort of context. Are you talking about transport in gases? Or say electrons in a 2DEG?

Regardless, "ballistic" usually means that the scattering length (the mean length a particle travels before being scattered) is of the same order of magnitude or larger than the device size (i.e. the space/surface it travels in/on). Diffuse transport means that the particle is being repeatedly scattered (see the "drunk student in a forest" problem in statistical physics).

3. Nov 18, 2016

### BvU

Why not give a link instead of search terms that lead nowhere (into a dark forest )

4. Nov 18, 2016

### f95toli

I don't have a link. However, it is a problem I've seen in several books. It is just "fun" version of the normal derivation of the random walk derivation of a diffusion equation, instead of a particle bouncing around in a graphyou imagine a very drunk student trying to find his/her way out of a circular forest. The "rules" are that the student will walk in a straight line until he/she walks into a tree and falls over, he/she will then get up and walk in a new random direction.
The goal of the exercise is to figure how far the student will have traveled after some time t (and when he/she will emerge from the forest).

Edit: A Google search for "random walk diffusion drunk" gives e.g. the following hit
http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L13/Lecture13.pdf

5. Nov 18, 2016

### KFC

Thanks for reference. It looks like a very good article to read.

When I first think of the problem, I am thinking of the transport in gas.