局域微扰的Loschillo回声：从费米-黄金法则到逃逸率区域的非单调交叉
Loschmidt echo for local perturbations: non-monotonous cross-over from the Fermi-golden-rule to the escape-rate regime
摘要：
我们通过考虑局部扰动的哈密顿量的Loschelles回声（LE）（或保真度）的时间衰减来解决量子力学时间演化的敏感性。在一个半经典的方法，我们推导出的LE衰减的混沌系统的整个范围从弱到强的局部扰动的解析表达式，并确定不同的衰减制度，补充那些已知的情况下的全局扰动。对于弱微扰，费米黄金法则（FGR）类型的行为被恢复。对于强扰动的逃逸率制度达到，LE指数衰减率独立的扰动强度。FGR制度和逃逸率制度之间的过渡是非单调的，即LE的指数时间衰减的速率作为扰动强度的函数振荡。我们进一步进行了广泛的量子力学计算的LE的基础上的数值波包演化，有力地支持了我们的半经典理论。最后，我们讨论了一些细节可能的实验实现观察预测的LE的行为。
英文摘要：
We address the sensitivity of quantum mechanical time evolution by considering the time decay of the Loschmidt echo (LE) (or fidelity) for local perturbations of the Hamiltonian. Within a semiclassical approach we derive analytical expressions for the LE decay for chaotic systems for the whole range from weak to strong local perturbations and identify different decay regimes which complement those known for the case of global perturbations. For weak perturbations a Fermi-golden-rule (FGR) type behavior is recovered. For strong perturbations the escape-rate regime is reached, where the LE decays exponentially with a rate independent of the perturbation strength. The transition between the FGR regime and the escape-rate regime is non-monotonic, i.e. the rate of the exponential time-decay of the LE oscillates as a function of the perturbation strength. We further perform extensive quantum mechanical calculations of the LE based on numerical wave packet evolution which strongly support our semiclassical theory. Finally, we discuss in some detail possible experimental realizations for observing the predicted behavior of the LE.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
