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Almost periodic Schrödinger operators IV. The Maryland model

Simon, Barry (1985) Almost periodic Schrödinger operators IV. The Maryland model. Annals of Physics, 159 (1). pp. 157-183. ISSN 0003-4916. doi:10.1016/0003-4916(85)90196-4.

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The analysis of discrete Schrödinger operators of the form (hu)(n) = u(n + 1) + u(n − 1) + λ tan(παn + θ) u(n) is discussed. Depending on Diophantine properties of α, the spectrum may be dense point, singular continuous or a mixture of the two.

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Simon, Barry0000-0003-2561-8539
Additional Information:© 1985 Published by Elsevier. Received March 5, 1984. Research partially supported by USNSF Grant MCS-81-20833. I would like to thank R. Prange for useful correspondence and his friendly encouragement, and T. Spencer and D. Thouless for useful discussions. Finally, I would like to express my tremendous debt of gratitude to J. Avron in connection with this paper. He suggested the model to me for further analysis and provided me with many useful discussions and comments on the manuscript. I regret that in the end he felt his contributions did not warrant his being a co-author of this paper.
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Official Citation:Barry Simon, Almost periodic Schrödinger operators IV. The maryland model, Annals of Physics, Volume 159, Issue 1, 1985, Pages 157-183, ISSN 0003-4916, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88112
Deposited By: George Porter
Deposited On:23 Jul 2018 18:05
Last Modified:16 Nov 2021 00:24

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