论文标题
倒谐波振荡器中的Krylov复杂性
Krylov complexity in inverted harmonic oscillator
论文作者
论文摘要
最近，已积极研究了额外订购的相关器（OTOC）和Krylov复杂性，以衡量运营商的生长。已知OTOC在混沌系统中表现出指数增长，这在许多以前的工作中都得到了证实。但是，在某些非核系统中，观察到OTOC显示出混乱的行为，无法区分以鞍形为主的混乱与混乱系统。对于k复杂性，在通用算子生长假说中，据说兰开斯系数显示出最快的混沌系统中线性生长。但是最近，似乎兰开斯系数和K-复合性在LMG模型中表现出混乱的行为，并且无法区分以鞍形为主的拼图与混乱。在本文中，我们计算倒置谐波振荡器中的兰斯佐斯系数和k复杂性。我们发现它们表现出混乱的行为，这与LMG模型的情况一致。我们还分析了量子Lyapunov系数和兰开斯系数的生长速率的界限，并发现混沌系统存在差异。还分析了微域K复合度，并将其与OTOC病例进行比较。
Recently, the out-of-time-ordered correlator(OTOC) and Krylov complexity have been studied actively as a measure of operator growth. OTOC is known to exhibit exponential growth in chaotic systems, which was confirmed in many previous works. However, in some non-chaotic systems, it was observed that OTOC shows chaotic behavior and cannot distinguish saddle-dominated scrambling from chaotic systems. For K-complexity, in the universal operator growth hypothesis, it was stated that Lanczos coefficients show linear growth in chaotic systems, which is the fastest. But recently, it appeared that Lanczos coefficients and K-complexity show chaotic behavior in the LMG model and cannot distinguish saddle-dominated scrambling from chaos. In this paper, we compute Lanczos coefficients and K-complexity in an inverted harmonic oscillator. We find that they exhibit chaotic behavior, which agrees with the case of the LMG model. We also analyze bounds on the quantum Lyapunov coefficient and the growth rate of Lanczos coefficients and find that there is a difference with the chaotic system. Microcanonical K-complexity is also analyzed and compared with the OTOC case.
