AI 中文总结
研究有限维量子系统中克里洛夫态复杂度动力学，利用基于离散能谱的正交多项式，发现其在低能态略超海森堡长度后停止增长，对其与二维量子引力中虫洞长度关系有重要意义。
AI 中文摘要
我们研究了有限维量子系统中克里洛夫态复杂度的动力学。基于离散能谱构建的正交多项式在大克里洛夫指数时远离态密度低的区域。该结果的物理意义是，即使使用在整个能谱上定义的极简克里洛夫态复杂度，在每个低能态中，克里洛夫复杂度在略超过海森堡长度后就停止增长。这对克里洛夫复杂度与二维量子引力中虫洞长度相关的提议有有趣的影响。
英文摘要
We study the dynamics of Krylov state complexity in finite-dimensional quantum systems. Orthogonal polynomials built on a discrete energy spectrum crowd away from regions where the density of states is low at large Krylov index. The physical implication of this result is that, even using a minimalist Krylov state complexity which is defined over the entire spectrum, the Krylov complexity provably stops growing a little past the Heisenberg length in every low-energy state. This has interesting implications for the proposal that Krylov complexity is related to the wormhole length in 2D quantum gravity.
Comments13+8 pages, 1 figure; v2: revised inequality
