Second-order corrections to mean-field evolution of weakly interacting Bosons, II

TL;DR

This paper extends previous work on Boson systems by removing interaction smallness assumptions and proving global existence of second-order correction solutions, leading to improved approximations of the N-body state.

Contribution

It introduces a global existence proof for second-order correction equations in Boson evolution without small interaction assumptions.

Findings

Proved global existence of solutions for the second-order correction equations.

Enhanced Fock-space estimates for the N-body Boson state approximation.

Extended the theoretical framework to handle larger interaction potentials.

Abstract

We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I, in which we derived a second-order correction to a mean-field evolution law for coherent states in the presence of small interaction potential. Here, we remove the assumption of smallness of the interaction potential and prove global existence of solutions to the equation for the second-order correction. This implies an improved Fock-space estimate for our approximation of the N-body state.