论文标题
操作员复杂性的普遍关系
Universal relation for operator complexity
论文作者
论文摘要
我们研究Krylov复杂性$ C_K $和操作员熵$ S_K $在运营商增长中。我们发现，对于各种系统，包括混乱的系统和综合理论，这两个数量总是享受对数关系$ s_k \ sim \ sim \ log {c_k} $，在长时间内，散发行为统一进化出现。否则，关系将不再存在。关系的普遍性与运营商增长的不可逆性密切相关。
We study Krylov complexity $C_K$ and operator entropy $S_K$ in operator growth. We find that for a variety of systems, including chaotic ones and integrable theories, the two quantities always enjoy a logarithmic relation $S_K\sim \log{C_K}$ at long times, where dissipative behavior emerges in unitary evolution. Otherwise, the relation does not hold any longer. Universality of the relation is deeply connected to irreversibility of operator growth.
