Cherenkov radiation with massive bosons and quantum friction

TL;DR

This paper develops a novel mathematical approach to analyze Cherenkov radiation and quantum friction effects in non-relativistic quantum field models, improving understanding of particle-field interactions and metastability.

Contribution

It introduces a new construction for Mourre conjugate operators that overcomes regularity issues in QFT models, applicable to multiple models including Nelson, Fröhlich's polaron, and quantum friction.

Findings

Improved bounds on metastability of the mass shell.

Enhanced applicability of Mourre's method to QFT models.

New insights into particle-field interaction effects.

Abstract

This work is devoted to several translation-invariant models in non-relativistic quantum field theory (QFT), describing a non-relativistic quantum particle interacting with a quantized relativistic field of bosons. In this setting, we aim at the rigorous study of Cherenkov radiation or friction effects at small disorder, which amounts to the metastability of the embedded mass shell of the free non-relativistic particle when the coupling to the quantized field is turned on. Although this problem is naturally approached by means of Mourre's celebrated commutator method, important regularity issues are known to be inherent to QFT models and restrict the application of this method. In this perspective, we introduce a novel non-standard construction procedure for Mourre conjugate operators, which differs from second quantization and allows to circumvent regularity issues. To show its versatility, we apply this construction to the Nelson model with massive bosons, to Fr\"ohlich's polaron model, and to a quantum friction model with massless bosons introduced by Bruneau and De Bi\`evre: for each of these examples, we improve on previous results.