[過去ﾛｸﾞ] 現代数学の系譜11 ガロア理論を読む23 [無断転載禁止]©2ch.net (1002ﾚｽ)
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589(1): 現代数学の系譜11 ガロア理論を読む 2016/10/05(水)06:31 ID:7cQ3hMXE(3/16) AAS
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外部ﾘﾝｸ[pdf]:www.nobelprize.org
Scientific Background Pdf 800 kB
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4 Quantum Hall conductance and topological band theory
The discovery of the integer quantum Hall effect was a milestone in the understanding
of the phases of matter. The Hall conductance in a very clean
(mobility about 10^5 cm2/Vs) two-dimensional electron gas cooled below 2 K
and subjected to a perpendicular magnetic field of the order of 15 T, was observed to obey the relation ・・・

(13)
where the first Chern number, C1, is known from the mathematics of fibre
bundles to be an integer. This explains why the conductance is quantized,
and why it is insensitive to perturbations such as disorder or interactions
between particles ? the Chern number is a topological invariant. It can only
be an integer! Using the explicit wave functions for the Landau problem, one
can explicitly calculate the integrals in Eq. (10), and show that C1 = 1 for any
filled Landau level.

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