{
  "abstract": "Every realistic quantum system is coupled to an environment. Including the environment restores a closed, Hermitian description, but at the cost of an intractably large Hilbert space. The Feshbach--Löwdin projection eliminates the unwanted degrees of freedom exactly, yielding an effective Hamiltonian $H_{\\rm eff}$ on the relevant subspace alone---which \\new{generically becomes non-Hermitian when the eliminated subspace contains an energetically accessible continuum and outgoing boundary conditions are imposed}. We illustrate this through a minimal model: a particle in a box with a delta barrier at its center. Direct elimination of one half-well reduces all information about the discarded sector to a single \\new{boundary parameter} $β$; the same result is then rederived via the Green's function and Dyson equation, offering a pedagogical illustration of how boundary data enter the Green's-function formalism and relating $β$ to a self-energy term. Whether $β$ is real or complex determines whether $H_{\\rm eff}$ is Hermitian or not, and the full range of behavior---from Hermitian dynamics through finite-width resonances to the counterintuitive quantum Zeno effect---follows from this single parameter.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Eur. J. Phys. 47, 055402 (2026)",
  "arxiv": "2611.05268",
  "author_total": 2,
  "authors": [
    {
      "name": "Ugo Lair"
    },
    {
      "name": "David Guéry-Odelin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1pv74hswqa6p7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05268",
  "fulltext_url": null,
  "id": "1pv74hswqa6p7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05268",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1pv74hswqa6p7.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.05268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05268"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Effective Hamiltonians and non-Hermitian physics",
  "title_text": "Effective Hamiltonians and non-Hermitian physics",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/1pv74hswqa6p7",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1088/1361-6404/ae9e99",
      "pid": "1v20srv6pyvfq",
      "relation": "published-as",
      "title": "Effective Hamiltonians and non-Hermitian physics",
      "venue": "European Journal of Physics"
    }
  ]
}