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| Content Provider | Springer Nature Link |
|---|---|
| Author | Damanik, David Lenz, Daniel |
| Copyright Year | 1999 |
| Abstract | In this Letter we introduce a method that allows one to prove uniform local results for one-dimensional discrete Schrödinger operators with Sturmian potentials. We apply this method to the transfer matrices in order to study the Lyapunov exponent and the growth rate of eigenfunctions. This gives uniform vanishing of the Lyapunov exponent on the spectrum for all irrational rotation numbers. For irrational rotation numbers with bounded continued fraction expansion, it gives uniform existence of the Lyapunov exponent on the whole complex plane. Moreover, it yields uniform polynomial upper bounds on the growth rate of transfer matrices for irrational rotation numbers with bounded density. In particular, all our results apply to the Fibonacci case. |
| Starting Page | 245 |
| Ending Page | 257 |
| Page Count | 13 |
| File Format | |
| ISSN | 03779017 |
| Journal | Letters in Mathematical Physics |
| Volume Number | 50 |
| Issue Number | 4 |
| e-ISSN | 15730530 |
| Language | English |
| Publisher | Kluwer Academic Publishers |
| Publisher Date | 1999-01-01 |
| Publisher Place | Dordrecht |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Group Theory and Generalizations Geometry Mathematical and Computational Physics Statistical Physics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistical and Nonlinear Physics Mathematical Physics |
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