Spectral transition line for the extended Harper’s model in the positive Lyapunov exponent regime. (English) Zbl 1390.81768
Summary: We study the spectral transition line of the extended Harper’s model in the positive Lyapunov exponent regime. We show that both pure point spectrum and purely singular continuous spectrum occur for dense subsets of frequencies on the transition line.
MSC:
| 81V70 | Many-body theory; quantum Hall effect |
| 82D20 | Statistical mechanics of solids |
| 78A25 | Electromagnetic theory (general) |
| 34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
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