Enhanced binding for a quantum particle coupled to scalar quantized field

TL;DR

This paper demonstrates enhanced binding for a quantum particle coupled to a scalar quantized field using functional integrals, revealing a localization phase transition in a statistical mechanics context.

Contribution

It introduces a new method employing functional integrals and Gaussian correlation inequality to prove enhanced binding in the single-particle scalar field coupling case.

Findings

Enhanced binding established for the scalar field case.

Describes a localization phase transition in a Brownian motion model.

Provides a new approach for analyzing particle-field interactions.

Abstract

Enhanced binding of a quantum particle coupled to a quantized field means that the Hamiltonian of the particle alone does not have a bound state, while the particle-field Hamiltonian does. For the Pauli--Fierz model, this is usually shown via the binding condition, which works less well in the case of a linear coupling to a scalar field. In particular, the case of a single particle linearly coupled to a scalar field has been open so far. Using a method relying on functional integrals and the Gaussian correlation inequality, we obtain enhanced binding for this case. From a statistical mechanics point of view, our result describes a localization phase transition (in the strength of the pair potential) for a Brownian motion subject to an external and an attractive pair potential.