{
  "abstract": "Josephson junctions are the central nonlinear element of superconducting qubits, yet their standard description is reached through a chain of approximations. We propose a purely quantum-mechanical model of the junction, formulated directly in Hilbert space: a charged particle moves on a one-dimensional loop, and the junction is a point at which the wave function obeys self-adjoint boundary conditions, labelled by a coupling strength $λ$, which controls the transparency of the junction, and a phase jump $δ$, which plays the role of the superconducting phase difference. For a loop with a single junction we solve the spectral problem and show that the ground-state momentum expectation, identified with the supercurrent, factorises exactly as $\\langle\\hat{p}_0\\rangle = I_c(δ,λ)\\sinδ$. For opaque junctions $I_c$ becomes independent of $δ$ and the first Josephson relation $I=I_c\\sinδ$ is recovered; for strongly attractive coupling, where the ground state is bound to the junction, the $\\sinδ$ law is also recovered, but with an exponentially suppressed amplitude. For more transparent junctions, however, the model \\emph{predicts} deviations from the pure $\\sinδ$ law: $I_c$ acquires a dependence on $δ$ already at order $λ^{-2}$, compatible with the higher Josephson harmonics recently found necessary to describe superconducting qubit spectra, and a fully transparent contact yields a current linear in $δ$. When the phase varies in time, a gauge transformation shows that the voltage drop across the junction is proportional to $\\dotδ$, so that the second Josephson relation emerges without being imposed. The boundary-condition approach thus reproduces both Josephson relations from first principles and predicts corrections to them, offering a route towards higher-fidelity models of superconducting qubits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13417",
  "author_total": 2,
  "authors": [
    {
      "name": "Luis Bueno Blanco"
    },
    {
      "name": "Juan Manuel Pérez-Pardo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5xfhgmtz8sfxw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13417",
  "fulltext_url": null,
  "id": "5xfhgmtz8sfxw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13417",
  "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",
      "cond-mat.supr-con"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7221549853",
  "pdf_url": "https://arxiv.org/pdf/2610.13417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5xfhgmtz8sfxw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.13417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13417"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.supr-con",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Modelling Josephson Junctions with Boundary Conditions: Towards High-Fidelity Models for Superconducting Qubits",
  "title_text": "Modelling Josephson Junctions with Boundary Conditions: Towards High-Fidelity Models for Superconducting Qubits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:36Z",
  "url": "https://research.draconitic.com/paper/5xfhgmtz8sfxw",
  "venue": "arXiv",
  "versions": []
}