论文标题
检测少数体量子混乱：饱和时的超时有序相关器
Detecting few-body quantum chaos: out-of-time ordered correlators at saturation
论文作者
论文摘要
我们通过数值和分析研究混乱的少数体量子力学系统中的超时有序相关器（OTOC）的时间依赖性和饱和度：量子4non-Heiles系统（弱混沌），BMN矩阵量子量子机制（强烈混乱）和Gaussian随机矩阵结合体。量子力学OTOC的生长模式是复杂且非宇宙的，在所研究的任何示例中，相关时间尺度上没有明确的指数状态（这与文献中有关多体系统的文献中发现的指数增长并不矛盾，即领域）。另一方面，长时间达到的OTOC的高原（饱和）值以简单而通用的方式随温度而降低：$ \ exp（\ mathrm {const。}/t^2）$ for for for弱chaos for for弱chaos的强烈混沌（包括随机矩阵）和$ \ exp（包括$ \ exp（包括$ \ exp。对于小型矩阵和足够复杂的操作员，还有另一个高温状态，饱和的OTOC随温度而生长。因此，高原OTOC值是几个体量子混乱的有意义的指标。我们还讨论了我们的发现对广告/CFT二元性的一些总体后果。
We study numerically and analytically the time dependence and saturation of out-of-time ordered correlators (OTOC) in chaotic few-body quantum-mechanical systems: quantum Henon-Heiles system (weakly chaotic), BMN matrix quantum mechanics (strongly chaotic) and Gaussian random matrix ensembles. The growth pattern of quantum-mechanical OTOC is complex and nonuniversal, with no clear exponential regime at relevant timescales in any of the examples studied (which is not in contradiction to the exponential growth found in the literature for many-body systems, i.e. fields). On the other hand, the plateau (saturated) value of OTOC reached at long times decreases with temperature in a simple and universal way: $\exp(\mathrm{const.}/T^2)$ for strong chaos (including random matrices) and $\exp(\mathrm{const.}/T)$ for weak chaos. For small matrices and sufficiently complex operators, there is also another, high-temperature regime where the saturated OTOC grows with temperature. Therefore, the plateau OTOC value is a meaningful indicator of few-body quantum chaos. We also discuss some general consequences of our findings for the AdS/CFT duality.
