Speaker
Julian Sonner
(Universite de Geneve (CH))
Description
We develop a classical counterpart of the Krylov complexity framework by running the Lanczos algorithm directly on the algebra of observables of a Hamiltonian system on a compact symplectic manifold. This construction arises naturally as the semiclassical limit of the quantum Lanczos algorithm. We demonstrate the usefulness of classical Krylov complexity in characterisation early-time dynamics in chaotic quantum systems with a semiclassical limit, and derive a Krylov-Ehrenfest theorem, which captures the eventual divergence of semiclassical and exact Krylov dynamics.