{
  "abstract": "Recent advances in microscopic many-body methods have enabled increasingly accurate descriptions of equilibrium quantum states, yet large-scale simulations of emergent-order dynamics typically rely on phenomenological equations with prescribed free-energy functionals. We introduce the Adiabatic Variational Principle (AVP), a framework for deriving order-parameter dynamics directly from an interacting many-body Hamiltonian. When microscopic relaxation is fast compared with order-parameter evolution, the many-body state follows the collective configuration adiabatically, in analogy with the Born--Oppenheimer separation of electronic and nuclear motion. This assumption makes explicit the adiabatic closure implicit in conventional phase-field descriptions. Each instantaneous order-parameter configuration then defines a constrained quasi-stationary many-body state, and the Lagrange multipliers enforcing these constraints directly provide the thermodynamic forces driving the collective evolution. Nonlinear Mori--Zwanzig projection theory further connects the reversible dynamics to the microscopic algebra of the collective variables and relates dissipation and fluctuations to the eliminated degrees of freedom. Applications to charge- and spin-density-wave dynamics recover Allen--Cahn domain growth, resolve evolving domain networks together with their microscopic electronic structure, and yield generalized Landau--Lifshitz dynamics for itinerant magnetism. The AVP thus provides a solver-independent microscopic foundation for phase-field-like simulations of the nonequilibrium dynamics of emergent electronic order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40117",
  "author_total": 6,
  "authors": [
    {
      "name": "Yang Yang"
    },
    {
      "name": "Ali Rayat"
    },
    {
      "name": "Ho Jang"
    },
    {
      "name": "Yunhao Fan"
    },
    {
      "name": "Sankha Subhra Bakshi"
    },
    {
      "name": "Gia-Wei Chern"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4n43gyxn0yyjj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40117",
  "fulltext_url": null,
  "id": "4n43gyxn0yyjj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40117",
  "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.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40117",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4n43gyxn0yyjj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40117",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40117"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Adiabatic Variational Principle: Born-Oppenheimer Theory for Emergent Electronic-Order Dynamics",
  "title_text": "Adiabatic Variational Principle: Born-Oppenheimer Theory for Emergent Electronic-Order Dynamics",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:47Z",
  "url": "https://research.draconitic.com/paper/4n43gyxn0yyjj",
  "venue": "arXiv",
  "versions": []
}