| Abstract: |
| We present lower bounds for Green`s function fractional moments of discrete random Schroedinger operators. These bounds take different forms, depending on whether the operator is local or non-local, and hold in various regimes of disorder and energy. We also extract consequences for the quantum dynamics and for the eigenfunction correlators.
In particular, we present regimes where the fractional Anderson model does not exhibit dynamical localization (finiteness of q-th moments of the averaged position operator for any given q ) even in the presence of pure point spectrum with polynomially decaying eigenfunctions. For the Anderson model, we show optimality of exponential decay of correlators at large disorder. Based on joint works with: 1) Constanza Rojas-Molina and Peter Hislop, and 2) Sergey Sergeev. |
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