{
  "abstract": "We characterize compactness of the Hilbert-Schmidt semigroups induced by finite-mode Gaussian quantum Markov semigroups with a faithful normal invariant state. A unitary second-quantization representation for every $ s $-embedding shows that compactness at one positive time, compact resolvent, drift stability, and uniqueness of the normal invariant state are equivalent. These conditions imply immediate trace-class membership for all embeddings. We derive exact trace-norm and Hilbert-Schmidt norm formulas, an embedding-independent trace identity, and the generator spectrum with algebraic multiplicities. Examples show that compactness does not require the existence of a spectral gap and that a spectral gap need not imply compactness when the invariant state is not unique.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13358",
  "author_total": 1,
  "authors": [
    {
      "name": "Zheng Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9aq9vdnmfeeyk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13358",
  "fulltext_url": null,
  "id": "9aq9vdnmfeeyk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13358",
  "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",
      "math.FA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7221539149",
  "pdf_url": "https://arxiv.org/pdf/2610.13358",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9aq9vdnmfeeyk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2610.13358",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13358"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Second quantization and compactness of induced Gaussian quantum Markov semigroups",
  "title_text": "Second quantization and compactness of induced Gaussian quantum Markov semigroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/9aq9vdnmfeeyk",
  "venue": "arXiv",
  "versions": []
}