Quantum Dynamics via Complex Analysis Methods: General Upper Bounds Without Time-Averaging and Tight Lower Bounds for the Strongly Coupled Fibonacci Hamiltonian
Quantum Dynamics via Complex Analysis Methods: General Upper Bounds Without Time-Averaging and Tight Lower Bounds for the Strongly Coupled Fibonacci Hamiltonian
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DOI：
10.1016/j.jfa.2008.08.010
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发表时间：
2008-01
期刊：
影响因子：
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通讯作者：
D. Damanik;Serguei Tcheremchantsev
中科院分区：
文献类型：
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作者：
D. Damanik;Serguei Tcheremchantsev
我们通过复变分析方法进一步发展了量子动力学上下界的方法，这是我们在一系列早期论文中介绍的。在这里，我们从复能量下转移矩阵的下界出发，导出了位置算子的非时间平均概率和矩的上界。此外，对于时间平均输运指数，我们在斐波那契哈密顿量的特殊情况下给出了改进的下界。这些界限导致了大耦合极限下波包快部分的时间平均扩散率的最佳描述。这提供了第一个例子，它证明了时间平均扩展速率可能超过频谱的上限盒计数维。
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities and moments of the position operator from lower bounds for transfer matrices at complex energies. Moreover, for the time-averaged transport exponents, we present improved lower bounds in the special case of the Fibonacci Hamiltonian. These bounds lead to an optimal description of the time-averaged spreading rate of the fast part of the wavepacket in the large coupling limit. This provides the first example which demonstrates that the time-averaged spreading rates may exceed the upper box-counting dimension of the spectrum.