弱量子混沌
Weak Quantum Chaos
摘要：
无序关联函数作为相互作用量子多体系统动力学混沌的量化因子，目前正受到广泛的讨论。我们认为，在量子自旋和费米子系统中，所有的本地运营商是有界的，一个OTOC的本地可观的是有界的，以及因此它的指数增长只是短暂的。作为一个更好的措施，在这样的系统中的量子混沌，我们提出，并研究，密度的OTOC广泛的本地观测量，它可以表现出无限的增长在热力学极限的总和。我们证明了这一点踢量子伊辛模型通过使用大规模的数值结果和可积制度的解析解。在一般情况下，我们观察到的OTOC密度的增长是线性的时间。我们证明，这种密度一般，局部相互作用，不可积的量子自旋和费米子动力学系统的增长表现出最多多项式的时间-一种现象，我们称之为弱量子混沌。在特殊情况下，该模型是可积的和所考虑的二次观测，OTOC密度饱和到一个平台。
英文摘要：
Out-of-time-ordered correlation functions (OTOC's) are presently being extensively debated as quantifiers of dynamical chaos in interacting quantum many-body systems. We argue that in quantum spin and fermionic systems, where all local operators are bounded, an OTOC of local observables is bounded as well and thus its exponential growth is merely transient. As a better measure of quantum chaos in such systems, we propose, and study, the density of the OTOC of extensive sums of local observables, which can exhibit indefinite growth in the thermodynamic limit. We demonstrate this for the kicked quantum Ising model by using large-scale numerical results and an analytic solution in the integrable regime. In a generic case, we observe the growth of the OTOC density to be linear in time. We prove that this density in general, locally interacting, non-integrable quantum spin and fermionic dynamical systems exhibits growth that is at most polynomial in time---a phenomenon, which we term weak quantum chaos. In the special case of the model being integrable and the observables under consideration quadratic, the OTOC density saturates to a plateau.
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