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.
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BibTeX
@misc{tishin2026local,
title = {{Local projective reconstruction of driven bosonic Hamiltonians}},
author = {A. M. Tishin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.22796},
eprint = {2605.22796},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.22796},
}
RIS
TY - UNPB
TI - Local projective reconstruction of driven bosonic Hamiltonians
AU - A. M. Tishin
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2605.22796
UR - https://arxiv.org/abs/2605.22796
AB - 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.
ER -