Abstract
It is shown how the Schrödinger equation for an electron in a two-dimensional periodic potential and a strong magnetic field can be reduced to a one-dimensional probe, in a potential with two different periods. The quantum Hall conductance is a topological invariant for this problem. This idea has been generalized to cover more realistic examples of the quantum Hall effect. This survey ends with a discussion of some striking but unexplained numerical results for the spectral measure for such a problem, and with some remarks on the fractional quantum Hall effect.
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© 1990 Springer-Verlag Berlin Heidelberg
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Thouless, D.J. (1990). The Quantum Hall Effect and the Schrödinger Equation with Competing Periods. In: Luck, JM., Moussa, P., Waldschmidt, M. (eds) Number Theory and Physics. Springer Proceedings in Physics, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75405-0_17
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DOI: https://doi.org/10.1007/978-3-642-75405-0_17
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