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 -