论文标题
在热力学稳定的远程相互作用系统中没有快速争夺
Absence of fast scrambling in thermodynamically stable long-range interacting systems
论文作者
论文摘要
在这项研究中，我们研究了具有幂律衰减相互作用的系统中的超级订单相关器（OTOC），例如$ r^{ - α} $，其中$ r $是距离。在这样的系统中，量子信息的快速争夺或信息传播的指数增长可能会根据衰减率$α$而发生。在这方面，至关重要的开放挑战是确定$α$的最佳条件，以免发生快速争夺。在这项研究中，我们在具有$α> d $（$ d $：空间尺寸）的通用远程相互作用系统中快速争夺，其中总能量在系统大小方面广泛，并且热力学极限定义明确。我们严格地证明，随着时间的推移，OTOC显示了多项式增长，并且在$ r $上的必要时间大于$ t \ gtrsim r^{\ frac {\ frac {2α-2D} {2α-d-dα-d+1}}} $。
In this study, we investigate out-of-time-order correlators (OTOCs) in systems with power-law decaying interactions such as $R^{-α}$, where $R$ is the distance. In such systems, the fast scrambling of quantum information or the exponential growth of information propagation can potentially occur according to the decay rate $α$. In this regard, a crucial open challenge is to identify the optimal condition for $α$ such that fast scrambling cannot occur. In this study, we disprove fast scrambling in generic long-range interacting systems with $α>D$ ($D$: spatial dimension), where the total energy is extensive in terms of system size and the thermodynamic limit is well-defined. We rigorously demonstrate that the OTOC shows a polynomial growth over time as long as $α>D$ and the necessary scrambling time over a distance $R$ is larger than $t\gtrsim R^{\frac{2α-2D}{2α-D+1}}$.
