Affine spin-pencil factorization of generalized driven anisotropic Rabi--Stark Hamiltonians in an…

Abstract

We construct a supersymmetric factorization for generalized driven anisotropic Rabi--Stark Hamiltonians using an affine factor Â=Ĉ+âD̂ in an inhomogeneous orthosymplectic superalgebra, with two real invertible spin matrices Ĉ and D̂. The six real pencil parameters constrain nine Hamiltonian frequencies and one energy offset up to an overall frequency scale. The normal product Â^†Â has an exact zero-energy ground doublet and, with its antinormal partner ÂÂ^†, gives a Witten index of two. For distinct pencil roots with finite baseline slopes, coherent gauges define a Bargmann hierarchy and endpoint conditions for exceptional finite-polynomial states. The spin grading organizes four limiting cases, comprising two driven-oscillator families with every baseline exact and the constrained anisotropic-Rabi and Rabi--Stark sheets, which meet at the degenerate-qubit isotropic Rabi model. An aligned interior example adds direct and longitudinal drives, Stark deformation, and intensity-dependent coupling while retaining the factorization.

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BibTeX

@misc{rodriguezlara2026affine,
  title = {{Affine spin-pencil factorization of generalized driven anisotropic Rabi--Stark Hamiltonians in an inhomogeneous orthosymplectic superalgebra}},
  author = {B. M. Rodriguez-Lara and F. H. Maldonado-Villamizar and A. Kafuri and A. Moroz},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36511},
  eprint = {2609.36511},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36511},
}

RIS

TY  - UNPB
TI  - Affine spin-pencil factorization of generalized driven anisotropic Rabi--Stark Hamiltonians in an inhomogeneous orthosymplectic superalgebra
AU  - B. M. Rodriguez-Lara
AU  - F. H. Maldonado-Villamizar
AU  - A. Kafuri
AU  - A. Moroz
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.36511
UR  - https://arxiv.org/abs/2609.36511
AB  - We construct a supersymmetric factorization for generalized driven anisotropic Rabi--Stark Hamiltonians using an affine factor Â=Ĉ+âD̂ in an inhomogeneous orthosymplectic superalgebra, with two real invertible spin matrices Ĉ and D̂. The six real pencil parameters constrain nine Hamiltonian frequencies and one energy offset up to an overall frequency scale. The normal product Â^†Â has an exact zero-energy ground doublet and, with its antinormal partner ÂÂ^†, gives a Witten index of two. For distinct pencil roots with finite baseline slopes, coherent gauges define a Bargmann hierarchy and endpoint conditions for exceptional finite-polynomial states. The spin grading organizes four limiting cases, comprising two driven-oscillator families with every baseline exact and the constrained anisotropic-Rabi and Rabi--Stark sheets, which meet at the degenerate-qubit isotropic Rabi model. An aligned interior example adds direct and longitudinal drives, Stark deformation, and intensity-dependent coupling while retaining the factorization.
ER  -

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