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I Harper-Hofstader Model

  1. Nov 4, 2016 #1
    How are Hofstader's Butterfly and Landau Levels in 2-Dimesnions related to each other, if at all ?
     
  2. jcsd
  3. Nov 9, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
  4. Nov 10, 2016 #3

    atyy

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  5. Nov 14, 2016 #4
  6. Nov 16, 2016 #5
    I'm currently writing a paper about Quantum Hall Effect, and I've run into these two concepts during my research. And as far as I am concerned, Landau level doesn't fully explain QHE and the "butterfly" is only remotely related. Quantum Hall effect is more of the result of mathematics than physics. The formulation of the resulting current in y direction under a weak electric filed in x direction, just so happens to consists of an integration that is mathematically proven to be an integer.
     
  7. Nov 17, 2016 #6
    Yes, I read that Hofstadter's butterfly is the result of the solution of the Harper's equation, which is just a particular case of a mathematical tool called Almost Mathieu Operator (i.e. λ = 1).
     
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