10.1007/978-3-030-01602-9_9
Leopold, Nikolai K
Nikolai K
Leopold
Pickl, Peter
Peter
Pickl
Mean-field limits of particles in interaction with quantised radiation fields
Springer
2018
2018-12-11T11:44:08Z
2019-08-02T12:36:48Z
conference
https://research-explorer.app.ist.ac.at/record/11
https://research-explorer.app.ist.ac.at/record/11.json
1806.10843
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.