{"paper":{"title":"Effective Dynamics for the Bose Polaron in the Large-Volume Mean-Field Limit","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The microscopic dynamics of the Bose polaron converge to the translation-invariant Bogoliubov-Fröhlich Hamiltonian in the large-volume mean-field limit.","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jonas Lampart, Peter Pickl, Siegfried Spruck","submitted_at":"2026-04-13T19:08:58Z","abstract_excerpt":"We consider the dynamics of the Bose polaron system, a dense quantum gas consisting of $N$ bosons evolving in $\\mathbb{R}^3$ in the presence of an impurity particle. The system is studied in the mean-field scaling with initially high density $\\rho$ and large volume $\\Lambda$ of the gas. In the initial state, almost all bosons are in the Bose-Einstein condensate, with a few excitations. We derive from the microscopic dynamics, in the joint limit of large densities and volumes, with the constraint $\\Lambda^3 \\ll \\rho$, the effective description by the translation-invariant Bogoliubov-Fr\\\"ohlich "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive from the microscopic dynamics, in the joint limit of large densities and volumes, with the constraint Λ³ ≪ ρ, the effective description by the translation-invariant Bogoliubov-Fröhlich Hamiltonian, which couples the quantum field of excitations linearly to the impurity particle.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The initial state consists of almost all bosons in the Bose-Einstein condensate with only a few excitations, combined with the specific scaling constraint Λ³ ≪ ρ that controls the mean-field limit.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"In the joint limit of large densities and volumes with Λ³ ≪ ρ, the microscopic Bose polaron dynamics converge to the translation-invariant Bogoliubov-Fröhlich Hamiltonian.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The microscopic dynamics of the Bose polaron converge to the translation-invariant Bogoliubov-Fröhlich Hamiltonian in the large-volume mean-field limit.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"24fb39d945f8196dfd706c5e568034147de6fc76086680904ca0dccca2f30daf"},"source":{"id":"2604.11976","kind":"arxiv","version":2},"verdict":{"id":"85bcfb95-ddb7-4819-b1a4-ef7d325ebb52","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T15:23:07.458897Z","strongest_claim":"We derive from the microscopic dynamics, in the joint limit of large densities and volumes, with the constraint Λ³ ≪ ρ, the effective description by the translation-invariant Bogoliubov-Fröhlich Hamiltonian, which couples the quantum field of excitations linearly to the impurity particle.","one_line_summary":"In the joint limit of large densities and volumes with Λ³ ≪ ρ, the microscopic Bose polaron dynamics converge to the translation-invariant Bogoliubov-Fröhlich Hamiltonian.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The initial state consists of almost all bosons in the Bose-Einstein condensate with only a few excitations, combined with the specific scaling constraint Λ³ ≪ ρ that controls the mean-field limit.","pith_extraction_headline":"The microscopic dynamics of the Bose polaron converge to the translation-invariant Bogoliubov-Fröhlich Hamiltonian in the large-volume mean-field limit."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.11976/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}