Syzranov S V, Gorshkov A V, Galitski V
Department of Physics, University of California, Santa Cruz, California 95064, USA.
Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.
Phys Rev B. 2018;97. doi: : 10.1103/PhysRevB.97.161114.
We study out-of-time-order correlators (OTOCs) of the form for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small region in a disordered interacting medium coupled to the rest of this medium considered as an environment. We demonstrate that for a system with discrete energy levels the OTOC saturates exponentially ∝Σ + const to a constant value at → ∞, in contrast with quantum-chaotic systems which exhibit exponential growth of OTOCs. Focusing on the case of a two-level system, we calculate microscopically the decay times and the value of the saturation constant. Because some OTOCs are immune to dephasing processes and some are not, such correlators may decay on two sets of parametrically different time scales related to inelastic transitions between the system levels and to pure dephasing processes, respectively. In the case of a classical environment, the evolution of the OTOC can be mapped onto the evolution of the density matrix of two systems coupled to the same dissipative environment.
我们研究了一个弱耦合到耗散环境的量子系统的非时序关联函数（OTOCs）。这样一个开放系统可以作为例如无序相互作用介质中的一个小区域的模型，该小区域与被视为环境的介质其余部分耦合。我们证明，对于具有离散能级的系统，OTOC在→∞时呈指数形式∝Σ + const饱和到一个恒定值，这与表现出OTOC指数增长的量子混沌系统形成对比。聚焦于两能级系统的情况，我们微观地计算了衰减时间和饱和常数的值。由于一些OTOC对退相过程免疫而一些则不然，此类关联函数可能在与系统能级之间的非弹性跃迁以及纯退相过程分别相关的两组参数不同的时间尺度上衰减。在经典环境的情况下，OTOC的演化可以映射到耦合到同一耗散环境的两个系统的密度矩阵的演化上。
