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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2407.14228 |
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| _version_ | 1866913437371596800 |
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| author | Haeming, Lian |
| author_facet | Haeming, Lian |
| contents | We obtain (up to logarithmic scaling) the power-law lower bound $M_{p}(T_{k})\gtrsim T_{k}^{(1-δ)p}$ on a subsequence $T_{k}\rightarrow\infty$, uniformly across $p>0$, for discrete one-dimensional quasiperiodic Schrödinger operators with frequencies satisfying $β(α)>\frac{3}δ\min_σγ$. We achieve this by obtaining a quantitative ballistic lower bound for the Abel-averaged time evolution of general periodic Schrödinger operators in terms of the bandwidths. A similar result without uniformity, which assumes $β(α)>\frac{C}δ\min_σγ$, was obtained earlier by Jitomirskaya and Zhang, for an implicit constant $C<\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14228 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasiballistic Transport for Discrete One-Dimensional Quasiperidic Schrödinger Operators Haeming, Lian Spectral Theory We obtain (up to logarithmic scaling) the power-law lower bound $M_{p}(T_{k})\gtrsim T_{k}^{(1-δ)p}$ on a subsequence $T_{k}\rightarrow\infty$, uniformly across $p>0$, for discrete one-dimensional quasiperiodic Schrödinger operators with frequencies satisfying $β(α)>\frac{3}δ\min_σγ$. We achieve this by obtaining a quantitative ballistic lower bound for the Abel-averaged time evolution of general periodic Schrödinger operators in terms of the bandwidths. A similar result without uniformity, which assumes $β(α)>\frac{C}δ\min_σγ$, was obtained earlier by Jitomirskaya and Zhang, for an implicit constant $C<\infty$. |
| title | Quasiballistic Transport for Discrete One-Dimensional Quasiperidic Schrödinger Operators |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2407.14228 |