Operator complexity: a journey to the edge of Krylov space

08.10.2020 14:00 – 15:00

The study of late time scales in black hole physics has triggered, in the frame of AdS/CFT correspondence, interest in the behavior of operator complexity beyond scrambling. Krylov complexity, or ‘K-complexity’ quantifies the growth of a given operator during Heisenberg evolution with respect to a special basis, generated by successive nested commutators of the Hamiltonian with the operator. In this talk I will present recent results on the evolution of K-complexity in finite-entropy systems for time scales greater than the scrambling time. I will discuss strict bounds on K-complexity as well as the associated Lanzcos sequence and show the results of a detailed numerical study of these quantities in the SYK-4 model, which is maximally chaotic, comparing them with the SYK-2 model, which is integrable. While the former saturates the bound, the latter stays exponentially below it, making it natural to conjecture that this is a generic feature of chaotic vs. integrable systems.

Lieu

Bâtiment: Ecole de Physique

Zoom meeting

entrée libre