What is a Phonon Mean Free Path? | Kittle's Solid-State Physics

[ehrenfest]

Homework Statement

My solid-state physics book (Kittel) talks about the phonon mean free path (on page 122) but never defines it. Can someone please give me a definition?

I know what a mean free path is for a non-quasi-particle but I do not see how that extends to phonons.

Homework Equations

The Attempt at a Solution

 

[genneth]

Why do you not think it applies to a quasi-particle but does for a "real" particle? Specifically, I'm intrigued as to your definition of a real vs quasi-particle.

 

[ehrenfest]

A quasi-particle like a phonon is not localized in space, is it? Therefore how can you define a path for it?

 

[genneth]

What makes you think real particles are any more localisable? The idea of a trajectory in quantum mechanics is just inherently dodgy. Anytime someone mentions trajectory, they're really using a short hand for something more subtle. In this case, it may mean for some semi-classical approximation, or by suitably defining the term "mean free path".

 

[merryjman]

Before I write, let me say I got most of this from the following site: http://www.cbu.edu/~jholmes/P353/N210ThermCond.doc

I think that the meaning here is similar to the concept of drift speed of electrons through a wire. Current flow can be macroscopically modeled as smooth, but at a molecular level a better model is one similar to the kinetic theory of gases; i.e. billiard balls colliding every which way but with a definite tendency to drift in one direction. So the phonon mean free path is the average distance a phonon 'particle' travels before 'colliding' with another particle. I read on the above-named site that the mean free path relates the temperature difference to the temperature gradient within the material, and the more phonons there are in an area, the more likely they are to collide with each other and therefore shorten the MFP.