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State--Generator Geometry of Open Quantum Systems: Compatibility and Covariant Transport — arXiv:2608.19175

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.19175
License (as archived): CC0-1.0
Archived: 2026-10-18T14:12:57.660Z
SHA-256 of the archived text: d8b33d431269243c00d6ae017ce9f5347a39d96b71f9a11b6a476fe362635513
Stable URL of this page: https://metraipolis.com/documento/dc_fdff0cc1576e

How to cite

State--Generator Geometry of Open Quantum Systems: Compatibility and Covariant Transport — arXiv:2608.19175 — arXiv (en), https://arxiv.org/abs/2608.19175 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fdff0cc1576e (Metraipolis archive dc_fdff0cc1576e, sha256 d8b33d431269243c00d6ae017ce9f5347a39d96b71f9a11b6a476fe362635513)

BibTeX

@misc{dcfdff0cc1576e,
  title = {State--Generator Geometry of Open Quantum Systems: Compatibility and Covariant Transport — arXiv:2608.19175},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.19175},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fdff0cc1576e; sha256 d8b33d431269243c00d6ae017ce9f5347a39d96b71f9a11b6a476fe362635513},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.19175. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We develop a geometry for transporting stationary-state response across the control space of an open quantum system. A physical model is represented by the ordered pair of its stationary state and dynamical generator. Embedding these pairs in a common ambient space induces a metric, a response one-form, and a closed two-form on the control manifold. The ambient space admits a canonical complex structure that exchanges state and generator directions, but the Liouvillian null-state condition restricts physical models to a submanifold that need not preserve this structure. For an amplitude-damped optical Bloch model, the metric and response two-form are compatible at the single point $\omega=0$ and $g/\Gamma=1/\sqrt{2}$; the physical manifold is non-Kähler elsewhere. The induced metric defines the Levi--Civita connection, geodesics, and parallel transport without requiring Kähler compatibility. We compute the connection by automatic differentiation through the stationary Liouvillian solve and recover the symbolic result to machine precision. A two-point calculation then shows that the resulting geodesic differs from linear interpolation in control space and follows a shorter path through the family of state--generator models. This geometry supplies the intrinsic derivative and transport structure needed to carry observable response, including multidimensional spectra, between admissible stationary models.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-08-20 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2608.19175 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T14:10:23.833Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-08-20?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).