论文标题
Krylov的复杂性
Krylov complexity in saddle-dominated scrambling
论文作者
论文摘要
在半古典系统中，据信超级订购相关器（OTOC）的指数增长被认为是量子混乱的标志。但是，在几次中，有人认为，即使在可集成的系统中，由于相位空间中存在不稳定的鞍点，OTOC也可以成倍增长。在这项工作中，我们探究了这种可集成的系统，该系统在Krylov的复杂性和相关的Lanczos系数中占主导地位。在通用算子生长假设的领域中，我们证明了兰开斯系数遵循线性生长，从而确保了Krylov复杂性在早期的指数行为。线性生长完全是由于鞍座而造成的，该鞍座占据了其他相位点，甚至远离自身。我们的结果表明，可以在具有鞍形为主的拼盘的可集成系统中观察到Krylov复杂性的指数增长，因此无需与混乱的存在有关。
In semi-classical systems, the exponential growth of the out-of-timeorder correlator (OTOC) is believed to be the hallmark of quantum chaos. However,on several occasions, it has been argued that, even in integrable systems, OTOC can grow exponentially due to the presence of unstable saddle points in the phase space. In this work, we probe such an integrable system exhibiting saddle dominated scrambling through Krylov complexity and the associated Lanczos coefficients. In the realm of the universal operator growth hypothesis, we demonstrate that the Lanczos coefficients follow the linear growth, which ensures the exponential behavior of Krylov complexity at early times. The linear growth arises entirely due to the saddle, which dominates other phase-space points even away from itself. Our results reveal that the exponential growth of Krylov complexity can be observed in integrable systems with saddle-dominated scrambling and thus need not be associated with the presence of chaos.
