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What is Localization?

Del Rio, R. and Jitomirskaya, S. and Last, Y. and Simon, B. (1995) What is Localization? Physical Review Letters, 75 (1). pp. 117-119. ISSN 0031-9007. doi:10.1103/PhysRevLett.75.117.

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We examine various issues relevant to localization in the Anderson model. We show there is more to localization than exponentially localized states by presenting an example with such states but where ⟨x(t)^2⟩/t^(2 − δ) is unbounded for any δ > 0. We show that the recently discovered instability of localization under rank one perturbations is only a weak instability.

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Simon, B.0000-0003-2561-8539
Additional Information:© 1995 American Physical Society. (Received 22 March 1995) We would like to thank J. Avron and A. Klein for useful discussions. The work of S.J. was supported by the National Science Foundation under Grant No. DMS-9208029. The work of B.S. was supported by the National Science Foundation under Grant No. DMS-9401491.
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Issue or Number:1
Classification Code:PACS numbers: 72.15.Rn
Record Number:CaltechAUTHORS:20180413-113435667
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85833
Deposited By: George Porter
Deposited On:13 Apr 2018 20:23
Last Modified:15 Nov 2021 20:32

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