Krylov complexity is a dynamical quantity of importance in holography and in the study of quantum chaos, operator growth and scrambling in many body systems. We extend the notion of Krylov complexity to time-dependent quantum systems. For periodic time-dependent (Floquet) systems, we give a natural and general method for doing the Krylov construction based on Arnoldi iteration and then define operator K-complexity for such systems. Focusing on kicked systems, in particular the quantum kicked rotor on a torus, we outline results of a detailed numerical study of the growth of the Krylov space dimension and the time dependence of Arnoldi coefficients as well as of the K-complexity when the coupling constant interpolates between the weak and strong coupling regime. Based on https://arxiv.org/abs/2305.00256 with Ankit Shrestha.
Zoom link: https://icts-res-in.zoom.us/j/88092766911?pwd=R3ZrVk9yeW96ZmQ4ZG9KRzVhenRKZz09
Meeting ID: 880 9276 6911
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