稀疏量子势垒对波函数的分割
Wave Function Shredding by Sparse Quantum Barriers
摘要：
我们讨论了一个模型，其中量子粒子通过$δ$势越来越稀疏的方式安排。对于无限多的障碍，我们推导出的条件，表示在各态历经性质的波函数阶段，确保点和绝对连续的部分是不存在的，留下一个纯粹的奇异连续谱。对于有限数量的障碍，透射系数显示出极端的敏感性粒子动量波动在许多不同的尺度。我们讨论了一个潜在的应用，这种行为所携带的信息擦除的波函数。
英文摘要：
We discuss a model in which a quantum particle passes through $δ$ potentials arranged in an increasingly sparse way. For infinitely many barriers we derive conditions, expressed in terms ergodic properties of wave function phases, which ensure that the point and absolutely continuous parts are absent leaving a purely singularly continuous spectrum. For a finite number of barriers, the transmission coefficient shows extreme sensitivity to the particle momentum with fluctuation in many different scales. We discuss a potential application of this behavior for erasing the information carried by the wave function.
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