Mean-field limits of particles in interaction with quantised radiation fields

N.K. Leopold, P. Pickl, in:, Springer, 2018, pp. 185–214.


Conference Paper | Published | English
Author
Department
Abstract
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.
Publishing Year
Date Published
2018-10-27
Volume
270
Page
185 - 214
Conference
MaLiQS: Macroscopic Limits of Quantum Systems
Conference Location
Munich, Germany
Conference Date
2017-03-30 – 2017-04-01
IST-REx-ID

Cite this

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
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
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.
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.
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.
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.

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