{
  "abstract": "We investigate the dynamics of full counting statistics (FCS) of the growth of the total number of fermions in a one-dimensional non-interacting lattice subjected to a localized particle gain (source) at one edge. The dynamics of the setup is modeled by the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) quantum master equation. We recast the counting problem that involves counting particle number at every lattice site to a problem where only the local injected site is involved. We employ the Schwinger-Keldysh path integral formalism within the GKSL framework and derive an analytical expression for the cumulant generating function at arbitrary times and obtain a Levitov-Lesovik type formula in the long-time limit, earlier derived for boundary driven setups in the steady-state. For clean lattices with either short- or long-range hopping, supporting single-particle delocalized eigenstates, we show that all cumulants grow linearly with time in the asymptotic regime. Our analytical results are in excellent agreement with direct numerical simulations. These findings establish a general framework for characterizing FCS and quantum fluctuations in driven open fermionic systems with localized particle injection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33724",
  "author_total": 2,
  "authors": [
    {
      "name": "Bijay Kumar Agarwalla"
    },
    {
      "name": "Manas Kulkarni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ax5jv0vk4rey2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33724",
  "fulltext_url": null,
  "id": "ax5jv0vk4rey2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33724",
  "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.mes-hall"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7214705554",
  "pdf_url": "https://arxiv.org/pdf/2609.33724",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ax5jv0vk4rey2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.33724",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33724"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Quantum Dynamics of Full Counting Statistics in Fermionic Lattices with Localized Gain",
  "title_text": "Quantum Dynamics of Full Counting Statistics in Fermionic Lattices with Localized Gain",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/ax5jv0vk4rey2",
  "venue": "arXiv",
  "versions": []
}