论文标题
开放量子系统中的操作员生长：耗散SYK的教训
Operator growth in open quantum systems: lessons from the dissipative SYK
论文作者
论文摘要
我们研究了开放量子系统的运算符增长，具有耗散耗散术语，扩大了Krylov的复杂性形式。 Rev. X 9，041017。我们的结果基于对由马尔可夫动力学管理的耗散$ q $ q $ q $ q $ - sachdev-ye-kitaev（Syk $ _Q $）模型。我们介绍了“操作员尺寸浓度”的概念，该概念允许在大$ $ q $限制中对两组Lanczos系数（$ a_n $和$ a_n $ and $ b_n $）的渐近线性行为进行渐近线性行为。我们的结果证实了大$ n $限制中有限$ q $的半分析学，以及有限$ q $和有限$ n $限制的数值arnoldi迭代。结果，Krylov的复杂性在饱和后表现出指数级的生长，该饱和度随着逆耗散强度而对数增长。与封闭的系统结果相比，抑制了复杂性的生长，但它在上限范围内订购的相关器（OTOC）的增长上限。我们对双重引力侧的结果提供了合理的解释。
We study the operator growth in open quantum systems with dephasing dissipation terms, extending the Krylov complexity formalism of Phys. Rev. X 9, 041017. Our results are based on the study of the dissipative $q$-body Sachdev-Ye-Kitaev (SYK$_q$) model, governed by the Markovian dynamics. We introduce a notion of ''operator size concentration'' which allows a diagrammatic and combinatorial proof of the asymptotic linear behavior of the two sets of Lanczos coefficients ($a_n$ and $b_n$) in the large $q$ limit. Our results corroborate with the semi-analytics in finite $q$ in the large $N$ limit, and the numerical Arnoldi iteration in finite $q$ and finite $N$ limit. As a result, Krylov complexity exhibits exponential growth following a saturation at a time that grows logarithmically with the inverse dissipation strength. The growth of complexity is suppressed compared to the closed system results, yet it upper bounds the growth of the normalized out-of-time-ordered correlator (OTOC). We provide a plausible explanation of the results from the dual gravitational side.
