A remark on the binding condition by the decay of particle's potential

TL;DR

This paper proves that the binding condition for a particle interacting with a Bose field is maintained through the decay of the particle's potential, leading to exponential decay of the ground state.

Contribution

It establishes a new link between potential decay and binding conditions in particle-Bose field systems, with implications for ground state properties.

Findings

Binding condition holds via potential decay

Ground state exhibits exponential decay

Potential decay ensures system stability

Abstract

The system of a particle interacting with a Bose field is investigated. It is proven that the binding condition holds by the decay of particle's potential. As an application, the exponential decay of the ground state follows.