Effective N-body dynamics for the massless Nelson model and adiabatic decoupling without spectral gap

TL;DR

This paper derives an effective N-body Schrödinger equation from the massless Nelson model without assuming weak coupling or a spectral gap, using a space-adiabatic theorem to control the adiabatic limit.

Contribution

It introduces a space-adiabatic theorem applicable without a spectral gap, enabling analysis of the Nelson model in a new scaling regime.

Findings

Derived effective N-body Schrödinger equation from the Nelson model.

Proved a space-adiabatic theorem without a spectral gap.

Established convergence control in the adiabatic limit.

Abstract

The Schroedinger equation for N particles interacting through effective pair potentials is derived from the massless Nelson model with ultraviolet cutoffs. We consider a scaling limit where the particles are slow and heavy, but, in contrast to earlier work [6], no ``weak coupling'' is assumed. To this end we prove a space-adiabatic theorem without gap condition which gives, in particular, control on the rate of convergence in the adiabatic limit.