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

  1. Jul 15, 2015 #1

    Andy Resnick

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    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:


    Or documents that merely state the results:

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

    Does anyone have a recommendation for something midway between these two extremes?
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  3. Jul 16, 2015 #2
  4. Jul 16, 2015 #3

    Andy Resnick

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  5. Jul 17, 2015 #4


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    "Noise and Fluctuations" by MacDonald is another option:


    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?



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

    Last edited by a moderator: May 7, 2017
  6. Jul 17, 2015 #5

    Andy Resnick

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    Thanks- I'll check those out.

    I pulled up Einsten'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:
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