波包扩展的动力学上界
Dynamical upper bounds on wavepacket spreading
摘要：
在薛定谔时间演化的框架下，我们得到了波包扩展速率的一般上界。我们的结果包括表明，一部分波包不能逃脱的球的大小动态增长的时间，这种增长的速度是由属性的谱测度和空间属性的解决方案的相关的时间无关的薛定谔方程。我们还得到了一个新的下限的扩散率，这是强有力的连接与我们的上界。我们应用这些新的界限的斐波那契哈密顿量-研究最多的一维模型的准晶。其结果是，我们得到了这个模型的上，下动态界建立波包扩散率之间的弹道运输和本地化。在大耦合的极限下，边界具有相同的定性行为。
英文摘要：
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 connected with our upper bound. We apply these new bounds to the Fibonacci Hamiltonian--the most studied one-dimensional model of quasicrystals. As a result, we obtain for this model upper and lower dynamical bounds establishing wavepacket spreading rates which are intermediate between ballistic transport and localization. The bounds have the same qualitative behavior in the limit of large coupling.
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