论文标题
条纹上安德森 - 定位本征函数的下限
Lower bounds on Anderson-localised eigenfunctions on a strip
论文作者
论文摘要
众所周知，随机schrödinger操作员在带状衰减上的特征函数呈指数型，并且衰减速率的速度并不比最慢的Lyapunov指数的规定慢。启发式论点的各种变化表明，没有比以此速度更快的征函数腐烂。我们迈出了这一猜想（在电势的分布足够规律的情况下），表明，对于每个特征功能，沿任何子序列的指数衰变速率严格慢于最快的Lyapunov指数，并且在沿途存在的lyapunov指数等于最慢的lyapunov指数。
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.
