The growth of operator entropy in operator growth

@article{Fan2022TheGO,
  title={The growth of operator entropy in operator growth},
  author={Zhong Fan},
  journal={Journal of High Energy Physics},
  year={2022},
  volume={2022},
  pages={1-16}
}
  • Z. Fan
  • Published 2 June 2022
  • Computer Science
  • Journal of High Energy Physics
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 |∂ t S K | ≤ 2 b 1 ∆ S K , where b 1 is the first Lanczos coefficient and ∆ S 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… 
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