Krylov meets Fock: Complementary lenses on quantum dynamics

arXiv:2611.05495v1 Announce Type: new Abstract: Quantum dynamics in Krylov space can be represented by a particle hopping on a chain whose sites are the Krylov basis vectors. The goal of this work is to extend this idea to the Fock basis, which in turn allows the description of a generic dynamics in terms of a more general, possibly higher-dimensional lattice. This construction has been dubbed the Fock state lattice (FSL), since its sites are identified with Fock states. To analyze the dynamics on the FSL we introduce various measures of the spread of a state, comparing them among themselves and with their Krylov counterparts. We apply our analysis to two models of light-matter interaction studied in quantum optics: the multi-mode Jaynes-Cummings and the Dicke models.