In other words, let’s choose the external magnetic... - Deepstash

In other words, let’s choose the external magnetic field we apply not rational , but only irrational . What can change, you might say. After all, there is only 0.5 difference between alpha=1/2 and alpha=1 . But that is not the case. The very interesting thing is that the butterfly only occurs for rational alpha values! If we plot the solutions of Harper’s equation corresponding to the irrational values of alpha ; we get nothing more than horizontal arrays of dots !

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