• Corpus ID: 235212380

On the spatial extent of localized eigenfunctions for random Schr\"odinger operators

  title={On the spatial extent of localized eigenfunctions for random Schr\"odinger operators},
  author={Fr{\'e}d{\'e}ric Klopp and Jeffrey H. Schenker},
The present paper is devoted to new, improved bounds for the eigenfunctions of random operators in the localized regime. We prove that, in the localized regime with good probability, each eigenfunction is exponentially decaying outside a ball of a certain radius, which we call the “localization onset length”. For ` > 0 large, we count the number of eigenfunctions having onset length larger than ` and find it to be smaller than exp(−C`) times the total number of eigenfunctions in the system… 

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