Local projective reconstruction of driven bosonic Hamiltonians

Abstract:Inferring a Hamiltonian from a single quantum trajectory is generally non-unique. This ambiguity limits inverse use of projective quantum geometry. Here we show that a nearest-neighbour structural prior makes the problem locally identifiable. For a smooth real time-dependent Jacobi Hamiltonian initialized at a ladder endpoint, the physical-time projective jet through order M+1 reconstructs the first M couplings, their logarithmic rates, and diagonal energy differences, up to an overall scalar-energy gauge. A canonical osculating-frame representation encodes the same data in a gauge-fixed connection. Pair-driven bosonic dynamics provides a direct realization because the vacuum evolves on the even-Fock Jacobi chain. In a nonstationary test, shallow reconstructions fit early projective data yet strongly overpredict later occupation growth; adding the projective order that resolves each hidden nonlinear layer restores the self-limited dynamics. The result supplies an inverse local counterpart to forward Krylov/Lanczos constructions and specifies when phase-resolved short-time state information identifies a sparse driven Hamiltonian.

15 pages. 1 figure

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

arXiv:2605.22796 [quant-ph]

(or arXiv:2605.22796v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.22796 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.