Simon, Barry and Zhu, Yunfeng (1996) The Lyapunov Exponents for Schrödinger Operators with Slowly Oscillating Potentials. Journal of Functional Analysis, 140 (2). pp. 541-556. ISSN 0022-1236. doi:10.1006/jfan.1996.0117. https://resolver.caltech.edu/CaltechAUTHORS:20170809-105308934
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Abstract
By studying the integrated density of states, we prove the existence of Lyapunov exponents and the Thouless formula for the Schrödinger operator –d^2/dx^2+cos x^ν with 0<ν<1 on L^2[0, ∞). This yields an explicit formula for these Lyapunov exponents. By applying rank one perturbation theory, we also obtain some spectral consequences.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1996 Academic Press. Received 14 August 1995, Accepted 2 November 1995. This material is based upon work supported by the National Science Foundation under Grant DMS-9401491. The Government has certain rights in this material. | |||||||||
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| Issue or Number: | 2 | |||||||||
| DOI: | 10.1006/jfan.1996.0117 | |||||||||
| Record Number: | CaltechAUTHORS:20170809-105308934 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170809-105308934 | |||||||||
| Official Citation: | Barry Simon, Yunfeng Zhu, The Lyapunov Exponents for Schrödinger Operators with Slowly Oscillating Potentials, Journal of Functional Analysis, Volume 140, Issue 2, 15 September 1996, Pages 541-556, ISSN 0022-1236, https://doi.org/10.1006/jfan.1996.0117. (http://www.sciencedirect.com/science/article/pii/S0022123696901172) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 80014 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 09 Aug 2017 17:58 | |||||||||
| Last Modified: | 15 Nov 2021 17:52 |
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