关于量子复兴，量子保真度，半经典方法
About Quantum Revivals, Quantum Fidelity, A semiclassical Approach
摘要：
本文讨论了近年来引起人们极大兴趣的量子递归和量子保真度问题。返回概率由给定的初始波包和相应的演化波包之间重叠的平方模给出;如果这种重叠是1，则可以观察到时间上的量子递归。我们提供了一些条件下，这是半经典实现作为初始波包的相干态位于相应的经典运动的封闭轨道。“量子保真度”（或洛施图回声）是演化的量子态与由轻微扰动的哈密顿量演化的相同量子态的重叠的平方模量。它在时间上的减少测量了量子演化相对于小扰动的敏感性。人们认为，当潜在的经典运动是混沌的或规则的时，它在时间上具有显著不同的行为。从合适的初始量子态开始，我们在线性响应框架（适用于小扰动制度）中发展了这种量子保真度的半经典估计，假设相应的经典运动具有遍历性条件。
英文摘要：
In this paper we develop the topics of Quantum Recurrences and of Quantum Fidelity which have attracted great interest in recent years. The return probability is given by the square modulus of the overlap between a given initial wavepacket and the corresponding evolved one; quantum recurrences in time can be observed if this overlap is unity. We provide some conditions under which this is semiclassically achieved taking as initial wavepacket a coherent state located on a closed orbit of the corresponding classical motion. The "quantum fidelity" (or Loschmidt Echo) is the square modulus of the overlap of an evoloved quantum state with the same evoloved by a slightly perturbed Hamiltonian. Its decrease in time measures the sensitivity of Quantum Evolution with respect to small perturbations. It is believed to have significantly different behavior in time when the underlying classical motion is chaotic or regular. Starting with suitable initial quantum states, we develop a semiclassical estimate of this quantum fidelity in the Linear Response framework (appropriate for the small perturbation regime), assuming some ergodicity conditions on the corresponding classical motion.
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