TY - JOUR

T1 - Lower Bounds on Anderson-Localised Eigenfunctions on a Strip

AU - Goldsheid, Ilya

AU - Sodin, Sasha

N1 - Publisher Copyright:
© 2022, The Author(s).

PY - 2022/5

Y1 - 2022/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85126111838&partnerID=8YFLogxK

U2 - 10.1007/s00220-022-04346-5

DO - 10.1007/s00220-022-04346-5

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C2 - 35529770

AN - SCOPUS:85126111838

SN - 0010-3616

VL - 392

SP - 125

EP - 144

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -