Würzburg Seminar on Quantum Field Theory and Gravity

Recently, there has been a renewed interest in studying state and operator dynamics in Krylov space.  This has been a fruitful pursuit, leading to novel probes of state and operator complexity and new avenues to study quantum chaosin many-body systems and holography. As measures of operator growth and complexity of states, Krylov and spread complexity respectively, have played a central role in the previous developments. In this talk, I will discuss some of their properties as probes of quantum chaos in quantum systems with finite and infinite dimensional Hilbert spaces. This talk is based on 2212.14702 , 2306.11632, 2405.11254 and upcoming work.