Dynamical Upper Bounds on Wavepacket Spreading

@inproceedings{KillipDynamicalUB,
  title={Dynamical Upper Bounds on Wavepacket Spreading},
  author={Rowan Killip and Alexander Kiselev and Yoram Last}
}
We derive a general upper bound on the spreading rate of wavepackets in the framework of Schrödinger time evolution. Our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically in time, where the rate of this growth is determined by properties of the spectral measure and by spatial properties of solutions of an associated time independent Schrödinger equation. We also derive a new lower bound on the spreading rate, which is strongly… CONTINUE READING
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