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Bandwidth statistics from the eigenvalue moments for the Harper–Hofstadter problem

Lipan, O. (2000) Bandwidth statistics from the eigenvalue moments for the Harper–Hofstadter problem. Journal of Physics A: Mathematical and General, 33 (39). pp. 6875-6888. ISSN 0305-4470.

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A method for studying the product of bandwidths for the Harper–Hofstader model is proposed, which requires knowledge of the moments of the midband energies. A general formula for these moments is conjectured, and the asymptotic representation for the product of bandwidths computed in the limit of a weak magnetic flux using Szeg¨o’s theorem for Hankel matrices. Then a first approximation for the edge of the butterfly spectrum is given and its connection with L´evy’s formula for Brownian motion discussed.

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Additional Information:© 2000 IOP Publishing Ltd. Received 24 January 2000, in final form 12 July 2000. I am grateful to P B Wiegmann for introducing me to this subject and for his many valuable comments and ideas. I would like to express my gratitude to B Simon for helpful discussions and for the fruitful scientific environment he created during the time this paper was written. I owe special thanks to A G Abanov, P Di Francesco, Y Last, V Sahakian, A Soshnikov and J Talstra, for stimulating discussions.
Subject Keywords:Mathieu equation, Bethe-ansatz, Bloch electrons, Wave Functions, Random Walk, Brownian Motion
Issue or Number:39
Record Number:CaltechAUTHORS:LIPjpa00
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:393
Deposited By: Archive Administrator
Deposited On:09 Jun 2005
Last Modified:02 Oct 2019 22:33

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