{
  "abstract": "We apply the momentous quantum mechanics formalism to the non-perturbative study of superconducting circuits in the transmon regime, deriving effective equations of motion for the bare Josephson junction (JJ), the cavity--JJ system, and a dissipative resonator. A Gaussian closure on the hierarchy of quantum moments resums the full cosine nonlinearity into the closed-form effective Hamiltonian $\\tfrac{1}{2}[V(ϕ+ϕ_s)+V(ϕ-ϕ_s)]$, which is non-perturbative and preserves the periodicity and boundedness of the Josephson potential at all phase amplitudes; the standard Kerr (Duffing) approximation is recovered as a special case. We derive the quantum-dressed frequency $ω_{\\rm eff}=Ω_p\\sqrt{\\cos(ϕ_{\\rm zpf}/ϕ_0)}$, and benchmark the effective dynamics against exact Mathieu-function diagonalization, with the quantum width $G^{2,0}(t)$ providing the most sensitive diagnostic of the closure's validity and marks the boundary of the Gaussian approximation more sharply than $\\langle\\hatϕ\\rangle(t)$ does. We compare the Caldirola--Kanai, Bateman, and Lindblad descriptions: the Bateman dynamics, quantized with a switched symplectic structure, preserves the Heisenberg bound, admits exact closed-form moment solutions, and reproduces the Lindblad benchmark for weak damping, i.e., within the analytic error bound $(λ/ω_1)^2\\,ϕ_{\\rm zpf}^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25296",
  "author_total": 3,
  "authors": [
    {
      "name": "Carlos Raul Javier Valdez"
    },
    {
      "name": "Hector Hugo Hernandez Hernandez"
    },
    {
      "name": "Guillermo Chacon-Acosta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4d41gxv1hv960.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25296",
  "fulltext_url": null,
  "id": "4d41gxv1hv960",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25296",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7214081436",
  "pdf_url": "https://arxiv.org/pdf/2609.25296",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4d41gxv1hv960.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25296",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25296"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Effective Study of Superconducting Quantum Circuits",
  "title_text": "Effective Study of Superconducting Quantum Circuits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/4d41gxv1hv960",
  "venue": "arXiv",
  "versions": []
}