RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan.
Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan.
Phys Rev E. 2018 Jan;97(1-1):012101. doi: 10.1103/PhysRevE.97.012101.
We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n-partite OTOCs as well as in the form of generalized covariance.
我们证明了一类具有修正统计平均的非时序相关量（OTOC）的广义涨落耗散定理，对于一般的热平衡量子系统，我们称之为双体 OTOC。通过一种称为维格纳-扬-塞克信息的量子涨落度量，可以量化双体 OTOC 与通常统计平均定义的物理 OTOC 之间的差异。在这个差异中，定理描述了量子系统中的混沌行为与涉及时间反转过程的非线性响应函数之间的普遍关系。我们表明，该定理可以推广到更高阶的 n 分体 OTOC 以及广义协方差的形式。
