Absence of Binding in the Nelson and Piezoelectric Polaron Models

TL;DR

This paper proves that in certain quantum models, such as the Nelson and piezoelectric polaron models, particles do not form bound states under specific conditions, and introduces improved criteria for no-binding in related models.

Contribution

It establishes a no-binding result for the Nelson and piezoelectric polaron models and improves the known conditions for optical bipolaron binding thresholds.

Findings

No binding occurs in the Nelson model with strong Coulomb repulsion.

The result applies to both renormalized and unrenormalized theories.

The methods reduce the no-binding condition threshold by about 30% for the optical bipolaron model.

Abstract

In the context of the massless Nelson model, we prove that two non-relativistic nucleons interacting with a massless meson field do not bind when a sufficiently strong Coulomb repulsion between the nucleons is added to the Hamiltonian. The result holds for both the renormalized and unrenormalized theories, and can also be applied to the so-called piezoelectric polaron model, which describes an electron interacting with the acoustical vibrational modes of a crystal through the piezoelectric interaction. The result can then be interpreted as well as a no-binding statement about piezoelectric bipolarons. The methods used allow also for a significant reduction of about 30% over previously known no-binding conditions for the optical bipolaron model of H. Fr\"ohlich.