论文标题
krylov的复杂性在calabi-yau量子力学
Krylov Complexity in Calabi-Yau Quantum Mechanics
论文作者
论文摘要
最近，提出了一种基于Lanczos算法和Krylov递归法的新型操作员生长复杂性的方法。我们研究了源自一些众所周知的局部曲折的calabi-yau几何形状以及一些非偏见模型的量子机械系统中的这种Krylov复杂性。我们发现，对于Calabi-Yau模型，兰开斯系数的生长比线性的$ n $ s慢，与可集成模型的行为一致。另一方面，对于非权益主义模型，兰开斯系数最初以小$ n $的线性线性生长，然后到达高原。尽管这看起来像是混乱的系统的行为，但正如文献中所说，这主要是由于鞍形为主的争夺效应所致。在我们的情况下，线性生长的兰开斯系数的斜率几乎使温度结合。在我们的研究期间，我们还为斜坡的结合提供了另一种一般推导。
Recently, a novel measure for the complexity of operator growth is proposed based on Lanczos algorithm and Krylov recursion method. We study this Krylov complexity in quantum mechanical systems derived from some well-known local toric Calabi-Yau geometries, as well as some non-relativistic models. We find that for the Calabi-Yau models, the Lanczos coefficients grow slower than linearly for small $n$'s, consistent with the behavior of integrable models. On the other hand, for the non-relativistic models, the Lanczos coefficients initially grow linearly for small $n$'s, then reach a plateau. Although this looks like the behavior of a chaotic system, it is mostly likely due to saddle-dominated scrambling effects instead, as argued in the literature. In our cases, the slopes of linearly growing Lanczos coefficients almost saturate a bound by the temperature. During our study, we also provide an alternative general derivation of the bound for the slope.
