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

Metadata

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.