We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Krylov complexity in Calabi–Yau quantum mechanics.
- Authors
Du, Bao-Ning; Huang, Min-Xin
- Abstract
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 nonrelativistic 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 nonrelativistic 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.
- Subjects
QUANTUM mechanics; LANCZOS method; KRYLOV subspace; CHAOS theory; TORIC varieties; QUANTUM chaos
- Publication
International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics, 2023, Vol 38, Issue 22/23, p1
- ISSN
0217-751X
- Publication type
Article
- DOI
10.1142/S0217751X23501269