From phase space to Krylov space: complexity and the geometry of chaos

          @misc{ scivideos_oai:cds.cern.ch:3025662,
            doi = {},
            url = {https://videos.cern.ch/record/3025662},
            author = {},
            keywords = {},
            language = {en},
            title = {From phase space to Krylov space: complexity and the geometry of chaos},
            publisher = {},
            year = {2026},
            month = {may},
            note = {oai:cds.cern.ch:3025662 see, \url{https://scivideos.org/cern-cds/3025662}}
          }
          

Abstract

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.

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