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

Autor:	Falconi, Marco, Leopold, Nikolai, Mitrouskas, David, Petrat, Sören
Rok vydání:	2021
Předmět:	Mathematical Physics Mathematics - Analysis of PDEs 35Q40 35Q55 81Q05 81T10 81V73 82C10
Druh dokumentu:	Working Paper
DOI:	10.1142/S0129055X2350006X
Popis:	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. Comment: 26 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2110.00458 Zobrazit plný text záznamu View this record from Arxiv