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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