Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.
Phys Rev Lett. 2018 Sep 21;121(12):124101. doi: 10.1103/PhysRevLett.121.124101.
Out-of-time-order correlators (OTOCs) have been proposed as sensitive probes for chaos in interacting quantum systems. They exhibit a characteristic classical exponential growth, but saturate beyond the so-called scrambling or Ehrenfest time τ_{E} in the quantum correlated regime. Here we present a path-integral approach for the entire time evolution of OTOCs for bosonic N-particle systems. We first show how the growth of OTOCs up to τ_{E}=(1/λ)logN is related to the Lyapunov exponent λ of the corresponding chaotic mean-field dynamics in the semiclassical large-N limit. Beyond τ_{E}, where simple mean-field approaches break down, we identify the underlying quantum mechanism responsible for the saturation. To this end we express OTOCs by coherent sums over contributions from different mean-field solutions and compute the dominant many-body interference term amongst them. Our method further applies to the complementary semiclassical limit ℏ→0 for fixed N, including quantum-chaotic single- and few-particle systems.
失序关联函数（OTOC）已被提议作为探测相互作用量子系统中混沌的灵敏探针。它们表现出特征性的经典指数增长，但在量子相关态下的所谓混频或 Ehrenfest 时间 τ_{E}之后会饱和。在这里，我们为玻色 N 粒子系统的 OTOC 的整个时间演化提供了一种路径积分方法。我们首先展示了 OTOC 增长到 τ_{E}=(1/λ)logN 与相应混沌平均场动力学的 Lyapunov 指数 λ之间的关系，在半经典大 N 极限中。在 τ_{E}之后，简单的平均场方法失效，我们确定了导致饱和的基本量子机制。为此，我们通过不同平均场解的相干求和来表示 OTOC，并计算它们之间的主要多体干涉项。我们的方法进一步适用于固定 N 的互补半经典极限 ℏ→0，包括量子混沌单粒子和少粒子系统。
