Bogoliubov Dynamics and Higherorder Corrections for the Regularized Nelson Model
Abstract
We study the time evolution of the Nelson model in a meanfield limit in which N nonrelativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higherorder corrections. More precisely, we prove the convergence of the approximate wave function to the manybody wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of PDEs describing the time evolution of the first and secondorder approximation to the oneparticle reduced density matrices of the particles and the quantum field, respectively.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.00458
 Bibcode:
 2021arXiv211000458F
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 35Q40;
 35Q55;
 81Q05;
 81T10;
 81V73;
 82C10
 EPrint:
 26 pages