Quasiballistic transport for discrete one-dimensional quasiperiodic Schrödinger operators
For discrete one-dimensional quasiperiodic Schrödinger operators with frequencies satisfying \beta(\alpha)>\bigl(\frac{3}{\delta}\bigr)\min_{\sigma}\gamma , we obtain (up to logarithmic scaling) the power-law lower bound M_{p}(T_{k})\gtrsim T_{k}^{(1-\delta)p} on a subsequence T_{k}\rightarrow\in...
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| Published in | Journal of spectral theory |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
29.08.2025
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| Online Access | Get full text |
| ISSN | 1664-039X 1664-0403 1664-0403 |
| DOI | 10.4171/jst/566 |
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| Summary: | For discrete one-dimensional quasiperiodic Schrödinger operators with frequencies satisfying \beta(\alpha)>\bigl(\frac{3}{\delta}\bigr)\min_{\sigma}\gamma , we obtain (up to logarithmic scaling) the power-law lower bound M_{p}(T_{k})\gtrsim T_{k}^{(1-\delta)p} on a subsequence T_{k}\rightarrow\infty , where \gamma is the associated Lyapunov exponent and \sigma is the spectrum. We achieve this by obtaining a quantitative ballistic lower bound for the Abel-averaged entries of the time evolution operator associated with general periodic Schrödinger operators in terms of the bandwidths. A similar result which assumes \beta(\alpha)>\bigl(\frac{C}{\delta}\bigr)\min_{\sigma}\gamma , was obtained earlier by Jitomirskaya and Zhang, for an implicit constant C<\infty . |
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| ISSN: | 1664-039X 1664-0403 1664-0403 |
| DOI: | 10.4171/jst/566 |