Author(s):

Leopold, Nikolai; Pickl, Peter

Title: 
Meanfield limits of particles in interaction with quantised radiation fields

Affiliation 
IST Austria 
Abstract: 
We report on a novel strategy to derive meanfield limits of quantum mechanical systems in which a large number of particles weakly couple to a secondquantized 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 oneparticle reduced density matrix of the nonrelativistic particles in Sobolev norm.

Keywords: 
Meanfield limit; Nelson model; SchrödingerKleinGordon system

Conference Title:

Workshop on Macroscopic Limits of Quantum Systems

Volume: 
270

Conference Dates:

March 30  April 1, 2017

Conference Location:

Munich, Germany

ISBN:

9783030016012

Publisher:

Springer

Location:

New York

Date Published:

20181027

Start Page: 
185

End Page:

214

DOI: 
10.1007/9783030016029_9

Open access: 
no 