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Homotopy and Quantization in Condensed Matter Physics

Avron, J. E. and Seiler, R. and Simon, B. (1983) Homotopy and Quantization in Condensed Matter Physics. Physical Review Letters, 51 (1). pp. 51-53. ISSN 0031-9007. doi:10.1103/PhysRevLett.51.51.

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It is shown that the integers found by Thouless et al. in the quantized Hall effect are the only quantized quantities associated with the energy bands. It is also proved that if two bands touch and then come apart as a parameter is varied, then their individual integers (conductances) may not be preserved but their sum is preserved.

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Simon, B.0000-0003-2561-8539
Additional Information:© 1983 American Physical Society. (Received 31 May 1983) We would like to thank P. Deift, R. Feynman, B.Fuller, R. Johnson, L. Romans, T. Spencer, B. Souillard, D. Thouless, G. Toulouse, J. Zak, and especially S. Cappell for useful discussions. We thank J. Sokoloff for drawing our attention to Ref. 13. This work was supported part in part through National Science Foundation Grant No. MCS-81-20833.
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Issue or Number:1
Classification Code:PACS numbers: 72.20.My, 02.40.+m, 71.25.-s
Record Number:CaltechAUTHORS:20180417-104513799
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85896
Deposited By: George Porter
Deposited On:17 Apr 2018 19:58
Last Modified:15 Nov 2021 20:33

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