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Overdamped vs underdamped Langevin

  1. Jan 16, 2014 #1
    If overdamped equation looks like
    ##\dot{x}_i=x_{i+1}+x_{i-1}-2x_i-V'(x_i)+F(t)##
    How to write down the underdamped Langevin equation
    ##\ddot{x}_i+\gamma\dot{x}_i=\gamma x_{i+1}+\gamma x_{i-1}-2 \gamma x_i-\gamma V'(x_i)+\gamma F(t)##
    Am I right?
     
  2. jcsd
  3. Jan 16, 2014 #2

    DrClaude

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    It does look like the ##\gamma## has been absorbed into the terms. But I guess it could have been used to redefine the length scale, so I'm sure that multiplying everything by ##\gamma## is the right thing to do. You have to go back to the derivation of the equation.

    And what does the index ##i## stand for?
     
  4. Jan 16, 2014 #3
    It labels particles. For example particle ##i## has neirest neighbours ##i-1## and ##i+1##.
     
  5. Jan 16, 2014 #4

    DrClaude

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    Then I really need more information on the physical system you are considering before I can be of any help.
     
  6. Jan 16, 2014 #5
    http://allariz.uc3m.es/~anxosanchez/ep/prb_50_9652_94.pdf [Broken]
     
    Last edited by a moderator: May 6, 2017
  7. Jan 16, 2014 #6

    DrClaude

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    Looking at equation (1) in that paper, they have the damping parameter ##\alpha##. I skimmed through the article, and couldn't find any indication that they are considering an overdamped regime, or indeed the first equation you gave in the OP.
     
  8. Jan 16, 2014 #7
    I known. But I'm interesting in that relation. Do you know some reference where I can find it? How could you always get from overdamped, underdamped and vice versa?
     
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