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

S. Teufel

Annales Henri Poincare 3 (2002), 939-965.
[Nelson3.ps (346.7 kB)]

Zusammenfassung

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, 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.