Diophantine equation in the integer quantum hall effect

[alex022]

Hi everybody!

I'm studying the IQHE and I want to understand the rise of the diophantine equation. I read the thouless article but it was no so conclusive.
I've also read the kohmoto article (phys rev B 1989) and he says that that property comes from the darboux theorem but i don't understand why… I've investigated the magnetic translation group but now I cannot do the link with the diophantine equation.

Can you help me?

Thanks a lot!

alex

 

[stone]

Here is a readable derivation of the diophantine equation in IQHE:
http://www.jstor.org/stable/51904?seq=8
See section 5 in particular

 

[stone]

See also the reference they cite for the derivation using magnetic translation group arguement.