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

Author(s): Leopold, Nikolai; Pickl, Peter
Title: Mean-field limits of particles in interaction with quantised radiation fields
Affiliation IST Austria
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.
Keywords: Mean-field limit; Nelson model; Schrödinger-Klein-Gordon system
Conference Title: Workshop on Macroscopic Limits of Quantum Systems
Volume: 270
Conference Dates: March 30 - April 1, 2017
Conference Location: Munich, Germany
ISBN: 978-303001601-2
Publisher: Springer  
Location: New York
Date Published: 2018-10-27
Start Page: 185
End Page: 214
DOI: 10.1007/978-3-030-01602-9_9
Open access: no
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