Lower Bounds on Anderson-Localised Eigenfunctions on a Strip

Ilya Goldsheid, Sasha Sodin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


It is known that the eigenfunctions of a random Schrödinger operator on a strip decay exponentially, and that the rate of decay is not slower than prescribed by the slowest Lyapunov exponent. A variery of heuristic arguments suggest that no eigenfunction can decay faster than at this rate. We make a step towards this conjecture (in the case when the distribution of the potential is regular enough) by showing that, for each eigenfunction, the rate of exponential decay along any subsequence is strictly slower than the fastest Lyapunov exponent, and that there exists a subsequence along which it is equal to the slowest Lyapunov exponent.

Original languageEnglish
Pages (from-to)125-144
Number of pages20
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - May 2022
Externally publishedYes


FundersFunder number
Horizon 2020 Framework Programme639305
Royal Society
European Research Council


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