Stability of quantum motion and correlation decay
Stability of quantum motion and correlation decay
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DOI：
10.1088/0305-4470/35/6/309
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发表时间：
2001-11
期刊：
影响因子：
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通讯作者：
T. Prosen;M. Znidaric
中科院分区：
文献类型：
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作者：
T. Prosen;M. Znidaric
我们导出了量子运动保真度和积分时间自相关函数之间的简单而一般的关系，该关系刻画了量子动力学对么正演化传播子的任意静态微扰的稳定性。令人惊讶的是，这种关系预示着保真度的衰退越慢，相关性的衰退就越快。特别是，对于不存在相关性渐近衰减的非遍历和非混合动力学，与发现保真度在时间尺度1/δ上指数衰减的混合动力学相反，在时间尺度1/δ上预测保真度的定性不同且更快的衰减，其中δ是扰动的强度。详细讨论了普朗克常数有效值较小的半经典区域，其中经典关联函数可以用来预测量子保真度衰变。请注意，在经典极限→0中恢复了正确且直观地预期的经典稳定性行为，因为两个极限δ→0和→0不互换。此外，我们还讨论了对自由度数的非平凡依赖性。所有的理论结果都在一个著名的量子化踢顶的例子中得到了清楚的数值演示。
We derive a simple and general relation between the fidelity of quantum motion, characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator, and the integrated time auto-correlation function of the generator of perturbation. Surprisingly, this relation predicts the slower decay of fidelity the faster the decay of correlations. In particular, for non-ergodic and non-mixing dynamics, where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a timescale 1/δ as opposed to mixing dynamics where the fidelity is found to decay exponentially on a timescale 1/δ2, where δ is the strength of perturbation. A detailed discussion of a semiclassical regime of small effective values of Planck constant is given where classical correlation functions can be used to predict quantum fidelity decay. Note that the correct and intuitively expected classical stability behaviour is recovered in the classical limit → 0, as the two limits δ → 0 and → 0 do not commute. In addition, we also discuss non-trivial dependence on the number of degrees of freedom. All the theoretical results are clearly demonstrated numerically on the celebrated example of a quantized kicked top.