“There’s a wonderful irony in this: the glorious precision with which these integers are measured is due to the dirty, crappy physics of impurities.” —– The Role of Disorder It turns out that the plateaux owe their existence to one further bit of physics: disorder. This arises because experimental samples are inherently dirty. They contain impurities which can be modelled by adding a random potential V(x) to the Hamiltonian. As we now explain, this random potential is ultimately responsible for the plateaux observed in the quantum Hall effect. There’s a wonderful irony in this: the glorious precision with which these integers are measured is due to the dirty, crappy physics of impurities. —– (I’m reading about the Quantum hall effect) http://www.damtp.cam.ac.uk/user/tong/qhe/two.pdf

“There’s a wonderful irony in this: the glorious precision with
which these integers are measured is due to the dirty, crappy physics of impurities.”
—–
The Role of Disorder

It turns out that the plateaux owe their existence to one further bit of physics: disorder.

This arises because experimental samples are inherently dirty. They contain impurities which can be modelled by adding a random potential V(x) to the Hamiltonian. As we
now explain, this random potential is ultimately responsible for the plateaux observed in the quantum Hall effect. There’s a wonderful irony in this: the glorious precision with
which these integers are measured is due to the dirty, crappy physics of impurities.
—–

(I’m reading about the Quantum hall effect)
http://www.damtp.cam.ac.uk/user/tong/qhe/two.pdf

Here’s a good reference about dirty topology, quantum hall effect and gauge invarience.

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