# Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model

## Metadata

### Rev. Math. Phys. 33, 2350006

The published version is available under subscription at World Scientific.

### arXiv 2110.00458

The preprint in pdf is available at arXiv.org.

### Bibtex

The bibtex entry for the article can be downloaded here.

## Abstract

We study the time evolution of the Nelson model in a mean-field limit in which \(N\) non-relativistic 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 higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body 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 second-order approximation to the one-particle reduced density matrices of the particles and the quantum field, respectively.