论文标题
操作员增长中操作员熵的增长
The growth of operator entropy in operator growth
论文作者
论文摘要
我们研究了运营商$ s_k $在运营商增长的上限。使用不确定性关系，我们首先证明了与增长率$ | \ partial_t s_k | \ leq2b_1Δs_k$限制的分散剂，其中$ b_1 $是第一个lanczos系数，$ΔS_K$是$ s_k $的差异。但是，对于不可逆转的过程，这种界限通常很长时间太松了。我们进一步发现，使用Krylov复杂性和操作员熵之间的通用对数关系，在很长的限制中更加紧密。新的边界在物理上有趣的情况（例如混沌系统和可集成的模型）中很好地描述了操作员熵的长时间行为。
We study upper bounds on the growth of operator entropy $S_K$ in operator growth. Using uncertainty relation, we first prove a dispersion bound on the growth rate $|\partial_t S_K|\leq 2b_1 ΔS_K$, where $b_1$ is the first Lanczos coefficient and $ΔS_K$ is the variance of $S_K$. However, for irreversible process, this bound generally turns out to be too loose at long times. We further find a tighter bound in the long time limit using a universal logarithmic relation between Krylov complexity and operator entropy. The new bound describes the long time behavior of operator entropy very well for physically interesting cases, such as chaotic systems and integrable models.
