Enhanced binding for N-particle system interacting with a scalar bose field I

TL;DR

This paper proves that an N-particle system interacting with a scalar Bose field can form a bound state with a ground state at large coupling constants, even if no ground state exists at zero coupling.

Contribution

It demonstrates the existence of a ground state for the system at sufficiently large coupling, using weak coupling limits and a modified HVZ theorem, without assuming ground state existence at zero coupling.

Findings

Existence of ground state at large coupling constants

Particles are bound by the scalar Bose field and external potentials

Application of weak coupling limit and modified HVZ theorem

Abstract

An enhanced binding of an $N$-particle system interacting through a scalar bose field is investigated, where $N\geq 2$. It is not assumed that this system has a ground state for a zero coupling. It is shown, however, that there exists a ground state for a sufficiently large values of coupling constants. When the coupling constant is sufficiently large, $N$ particles are bound to each other by the scalar bose field, and are trapped by external potentials. Basic ideas of the proofs in this paper are applications of a weak coupling limit and a modified HVZ theorem.