2024/01/14 by Hislop, Peter D>, Kirsch, Werner, Krishna, M.
#81Q10 81Q05 35J10 #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2401.07262
We provide a simple proof of dynamical delocalization, that is, time-increasing lower bounds on quantum transport for discrete, one-particle Schrodinger operators on ℓ2 (ℤd), provided solutions to the Schrodinger equation satisfy certain growth conditions. The proof is based on basic resolvent identities and the Combes-Thomas estimate on the exponential decay of the Green's function. As a consequence, we prove that generalized eigenfunctions for energies outside the spectrum of H must grow exponentially in some directions. We also prove that if H has any absolutely continuous spectrum, then the Schrodinger operator exhibits dynamical delocalization. We apply the general result to Γ-trimmed Schrodinger operators, with periodic Γ, and prove dynamical delocalization for these operators. These results also apply to the Γ-trimmed Anderson model, providing a random, ergodic model exhibiting both dynamical localization in an energy interval and dynamical delocalization.