How are Hofstadter's butterfly and Landau levels in 2D related?

[VishalSharma]

How are Hofstader's Butterfly and Landau Levels in 2-Dimesnions related to each other, if at all ?

 

[atyy]

I googled your keywords and found http://online.kitp.ucsb.edu/online/colloq/kim1/

 

[VishalSharma]

I googled your keywords and found http://online.kitp.ucsb.edu/online/colloq/kim1/

Thanks for your help!

 

[Xu Shuang]

Thanks for your help!

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.

 

[VishalSharma]

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).