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- W4296594554 abstract "Let $mathcal{L}$ be a fixed $d$-dimensional lattice. We study the localization properties of solutions of the stationary Schrodinger equation with a positive $L^infty$ potential on tori $mathbb{R}^d/Lmathcal{L}$ in the limit, as $Ltoinfty$, for dimension $d leq 3$. We show that the probability measures associated with $L^2$-normalized solutions, with eigenvalue $E$ near the bottom of the spectrum, satisfy an algebraic delocalization theorem which states that these probability measures cannot be localized inside a ball of radius $r = o(E^{-1/4+epsilon})$, unless localization occurs with a sufficiently slow algebraic decay. In particular, we apply our result to Schrodinger operators modeling disordered systems, such as the d-dimensional continuous Anderson- Bernoulli model, where almost sure exponential localization of eigenfunctions, in the limit as $E to 0$, was proved by Bourgain-Kenig in dimension $d geq 2$, and show that our theorem implies an algebraic blow-up of localization length in this limit." @default.
- W4296594554 created "2022-09-22" @default.
- W4296594554 creator A5002272562 @default.
- W4296594554 date "2022-09-20" @default.
- W4296594554 modified "2023-10-14" @default.
- W4296594554 title "Algebraic delocalization for the Schrodinger equation on large tori" @default.
- W4296594554 doi "https://doi.org/10.48550/arxiv.2209.09672" @default.
- W4296594554 hasPublicationYear "2022" @default.
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