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

Abstract

An enhanced binding of an N -particle system linearly coupled to a scalar bose field is investigated, where N ≥ 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 sufficiently large values of a coupling constant. Basic ingredients of the proof are a weak coupling limit and a modified HVZ theorem.

Existence of a ground state for the Nelson model with a singular perturbation

“…Gérard [9] also shows the similar result, but the method is different from [23]. Hiroshima and Sasaki [17] shows the enhanced binding of the many body Nelson model, i.e.,the existence of ground states is shown for sufficiently large couplings but the existence of ground state of decoupled Hamiltonian is not assumed.…”

Enhanced Binding of an $N$-particle System Interacting with a Scalar Field II. Relativistic Version

“…If K 0 + αK I with sufficiently large coupling constants has a ground state whether K 0 has a ground state or not, then it is said that enhanced binding occurs. Enhanced binding is initiated by [HS01] and in the previous paper [HS08] enhanced binding is shown for a system of N-nonrelativistic particles governed by Schödinger operator and linearly coupled to a massless scalar bose field. In this paper replacing the nonrelativistic particles with relativistic ones, we show the enhanced binding.…”

“…For general V we can prove the theorem by the same limiting argument as [HS08,Appendix]. See Appendix B…”

“…These are proven by energy comparison inequality derived by functional integration of the heat semigroup generated by (1.3) (Lemma 3.2) and a simple variation principle (Lemma 3.3), hence we focus on showing the stability condition on h V eff instead of H V . (Uniform exponential localization by functional integrations) Our method is a minor but nontrivial modification of [HS08] and a mixture of [Gér00,GLL01]. We do not assume the compactness condition on H p , which is entered in [Gér00].…”

On the ionization energy of the semi-relativistic Pauli-Fierz model for a single particle

“…In the quantum field theory one important task is to show the existence of ground states, which is shown in general by showing or assuming the positivity of an ionization energy. See e.g., [1,2,5,9].…”