{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2305.06722"}],"oa":1,"publication_status":"epub_ahead","oa_version":"Preprint","publication":"Annales de l'Institut Henri Poincaré C","_id":"20045","DOAJ_listed":"1","department":[{"_id":"RoSe"}],"date_updated":"2025-07-23T07:23:06Z","doi":"10.4171/aihpc/154","article_type":"original","language":[{"iso":"eng"}],"day":"06","OA_place":"repository","publication_identifier":{"issn":["0294-1449"],"eissn":["1873-1430"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","author":[{"first_name":"Marco","last_name":"Falconi","full_name":"Falconi, Marco"},{"full_name":"Lampart, Jonas","last_name":"Lampart","first_name":"Jonas"},{"full_name":"Leopold, Nikolai","last_name":"Leopold","first_name":"Nikolai"},{"first_name":"David Johannes","last_name":"Mitrouskas","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes"}],"month":"05","external_id":{"arxiv":["2305.06722"]},"date_published":"2025-05-06T00:00:00Z","title":"Renormalized Bogoliubov theory for the Nelson model","article_processing_charge":"No","OA_type":"green","citation":{"apa":"Falconi, M., Lampart, J., Leopold, N., &#38; Mitrouskas, D. J. (2025). Renormalized Bogoliubov theory for the Nelson model. <i>Annales de l’Institut Henri Poincaré C</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/aihpc/154\">https://doi.org/10.4171/aihpc/154</a>","mla":"Falconi, Marco, et al. “Renormalized Bogoliubov Theory for the Nelson Model.” <i>Annales de l’Institut Henri Poincaré C</i>, European Mathematical Society, 2025, doi:<a href=\"https://doi.org/10.4171/aihpc/154\">10.4171/aihpc/154</a>.","short":"M. Falconi, J. Lampart, N. Leopold, D.J. Mitrouskas, Annales de l’Institut Henri Poincaré C (2025).","chicago":"Falconi, Marco, Jonas Lampart, Nikolai Leopold, and David Johannes Mitrouskas. “Renormalized Bogoliubov Theory for the Nelson Model.” <i>Annales de l’Institut Henri Poincaré C</i>. European Mathematical Society, 2025. <a href=\"https://doi.org/10.4171/aihpc/154\">https://doi.org/10.4171/aihpc/154</a>.","ama":"Falconi M, Lampart J, Leopold N, Mitrouskas DJ. Renormalized Bogoliubov theory for the Nelson model. <i>Annales de l’Institut Henri Poincaré C</i>. 2025. doi:<a href=\"https://doi.org/10.4171/aihpc/154\">10.4171/aihpc/154</a>","ista":"Falconi M, Lampart J, Leopold N, Mitrouskas DJ. 2025. Renormalized Bogoliubov theory for the Nelson model. Annales de l’Institut Henri Poincaré C.","ieee":"M. Falconi, J. Lampart, N. Leopold, and D. J. Mitrouskas, “Renormalized Bogoliubov theory for the Nelson model,” <i>Annales de l’Institut Henri Poincaré C</i>. European Mathematical Society, 2025."},"publisher":"European Mathematical Society","date_created":"2025-07-21T07:59:16Z","type":"journal_article","abstract":[{"text":"We consider the time evolution of the renormalized Nelson model, which describes N bosons linearly coupled to a quantized scalar field, in the mean-field limit of many particles N≫1 with coupling constant proportional to N^−1/2. First, we show that initial states exhibiting Bose–Einstein condensation for the particles and approximating a coherent state for the quantum field retain their structure under the many-body time evolution. Concretely, the dynamics of the reduced densities are approximated by solutions of two coupled PDEs, the Schrödinger–Klein–Gordon equations. Second, we construct a renormalized Bogoliubov evolution that describes the quantum fluctuations around the Schrödinger–Klein–Gordon equations. This evolution is used to extend the approximation of the evolved many-body state to the full norm topology. In summary, we provide a comprehensive analysis of the Nelson model that reveals the role of renormalization in the mean-field Bogoliubov theory.","lang":"eng"}],"arxiv":1,"year":"2025","status":"public"}