Q: Fokker-Planck (Brownian motion) for undergrads?

[Andy Resnick]

All,

I'm looking for a reference to help guide one of my students- a motivated physics undergrad. I would like him to work through a derivation of the mean-squared displacement of a particle undergoing free Brownian motion (free diffusion) and then for a particle held in an optical trap.

All of the references I have are graduate-level, and a quick google search turns up either mathematically-oriented derivations:

http://physics.gu.se/~frtbm/joomla/media/mydocs/LennartSjogren/kap7.pdf
http://wwwf.imperial.ac.uk/~pavl/lec_fokker_planck.pdf

Or documents that merely state the results:

http://faculty.philau.edu/masoodir/PDF/Projects/Thermo/Brownian%20Motion.pdf

Does anyone have a recommendation for something midway between these two extremes?

 

[William White]

from first principles, to the randomnm walk (mean squared displacement) to the diffusion equation:

http://www.amazon.com/dp/0749266953/?tag=pfamazon01-20

 

[Andy Resnick]

Thanks!

 

[jasonRF]

"Noise and Fluctuations" by MacDonald is another option:

https://www.amazon.com/dp/0486450295/?tag=pfamazon01-20

If I recall correctly, it should be readable by an upper division undergrad (but then I read it after grad school so my perspective may be off).

It's been awhile since I've looked at them, but I wonder how readable Einstein's original papers are ... might be inspiring to read the original, perhaps after the basic calculation is understood?

jason

EDIT:

There is also a book by Lemons that I have only flipped through - may be worth a look but I haven't read it:

https://www.amazon.com/dp/080186867X/?tag=pfamazon01-20

 

[Andy Resnick]

Thanks- I'll check those out.

I pulled up Einstein's paper: the result of interest is in section 4, but the reasoning is difficult to follow (the relevant sentence reminds me of the cartoon '...then a miracle occurs"). On the other hand, this looks promising:
http://www.maths.qmul.ac.uk/~klages/people/msc_qirezi.pdf