--- _id: '11' abstract: - lang: eng text: We report on a novel strategy to derive mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. The technique combines the method of counting and the coherent state approach to study the growth of the correlations among the particles and in the radiation field. As an instructional example, we derive the Schrödinger–Klein–Gordon system of equations from the Nelson model with ultraviolet cutoff and possibly massless scalar field. In particular, we prove the convergence of the reduced density matrices (of the nonrelativistic particles and the field bosons) associated with the exact time evolution to the projectors onto the solutions of the Schrödinger–Klein–Gordon equations in trace norm. Furthermore, we derive explicit bounds on the rate of convergence of the one-particle reduced density matrix of the nonrelativistic particles in Sobolev norm. author: - first_name: Nikolai K full_name: Leopold, Nikolai K id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87 last_name: Leopold orcid: 0000-0002-0495-6822 - first_name: Peter full_name: Pickl, Peter last_name: Pickl citation: ama: 'Leopold NK, Pickl P. Mean-field limits of particles in interaction with quantised radiation fields. In: Vol 270. Springer; 2018:185-214. doi:10.1007/978-3-030-01602-9_9' apa: 'Leopold, N. K., & Pickl, P. (2018). Mean-field limits of particles in interaction with quantised radiation fields (Vol. 270, pp. 185–214). Presented at the MaLiQS: Macroscopic Limits of Quantum Systems, Munich, Germany: Springer. https://doi.org/10.1007/978-3-030-01602-9_9' chicago: Leopold, Nikolai K, and Peter Pickl. “Mean-Field Limits of Particles in Interaction with Quantised Radiation Fields,” 270:185–214. Springer, 2018. https://doi.org/10.1007/978-3-030-01602-9_9. ieee: 'N. K. Leopold and P. Pickl, “Mean-field limits of particles in interaction with quantised radiation fields,” presented at the MaLiQS: Macroscopic Limits of Quantum Systems, Munich, Germany, 2018, vol. 270, pp. 185–214.' ista: 'Leopold NK, Pickl P. 2018. Mean-field limits of particles in interaction with quantised radiation fields. MaLiQS: Macroscopic Limits of Quantum Systems vol. 270, 185–214.' mla: Leopold, Nikolai K., and Peter Pickl. Mean-Field Limits of Particles in Interaction with Quantised Radiation Fields. Vol. 270, Springer, 2018, pp. 185–214, doi:10.1007/978-3-030-01602-9_9. short: N.K. Leopold, P. Pickl, in:, Springer, 2018, pp. 185–214. conference: end_date: 2017-04-01 location: Munich, Germany name: 'MaLiQS: Macroscopic Limits of Quantum Systems' start_date: 2017-03-30 date_created: 2018-12-11T11:44:08Z date_published: 2018-10-27T00:00:00Z date_updated: 2021-01-12T06:48:16Z day: '27' department: - _id: RoSe doi: 10.1007/978-3-030-01602-9_9 ec_funded: 1 external_id: arxiv: - '1806.10843' intvolume: ' 270' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1806.10843 month: '10' oa: 1 oa_version: Preprint page: 185 - 214 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication_status: published publisher: Springer publist_id: '8045' quality_controlled: '1' scopus_import: 1 status: public title: Mean-field limits of particles in interaction with quantised radiation fields type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 270 year: '2018' ...