量子弹道和扩散晶格系统中的分形噪声
Fractal Noise in Quantum Ballistic and Diffusive Lattice Systems
摘要：
我们证明了在周期和准周期紧束缚晶格中，波包分别以弹道或扩散方式运动的量子演化中的分形噪声。对于弹道的情况下，各种初始叠加，我们得到了时空自仿射分形$Ψ(x,t)$，验证了贝里的预测“一个粒子在一个盒子”，除了量子复兴。对于扩散的情况下，自相似分形演化也得到了。量子理论的这些普遍分形特征在量子信息领域可能是有用的，用于创建有效的量子算法，并且可能在纳米结构的散射中被检测到。
英文摘要：
We demonstrate fractal noise in the quantum evolution of wave packets moving either ballistically or diffusively in periodic and quasiperiodic tight-binding lattices, respectively. For the ballistic case with various initial superpositions we obtain a space-time self-affine fractal $Ψ(x,t)$ which verify the predictions by Berry for "a particle in a box", in addition to quantum revivals. For the diffusive case self-similar fractal evolution is also obtained. These universal fractal features of quantum theory might be useful in the field of quantum information, for creating efficient quantum algorithms, and can possibly be detectable in scattering from nanostructures.
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