---
_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'
...