Infrared Problem in Cold Atom Quantum Physisorption on 2D Materials

TL;DR

This paper compares four theoretical approaches to phonon-assisted quantum adsorption of cold atoms on 2D materials, highlighting that only the soft-phonon resummation method remains divergence-free at large membrane sizes and finite temperatures.

Contribution

It introduces and evaluates four different approximation methods for the adsorption rate, identifying the SPR method as the only divergence-free approach in large membrane regimes.

Findings

Only the SPR method yields a finite adsorption rate at large membrane sizes.

The other three methods diverge in the limit of an infinite surface.

The study clarifies the limitations of common approximation techniques in this context.

Abstract

Results from four different approximations to the phonon-assisted quantum adsorption rate for cold atoms on a 2D material are compared and contrasted: (1) a loop expansion (LE) based on the atom-phonon coupling, (2) non-crossing approximation (NCA), (3) independent boson model approximation (IBMA), and (4) a leading-order soft-phonon resummation method (SPR). We conclude that, of the four approximations considered, only the SPR method gives a divergence-free result in the large membrane regime at finite temperature. The other three methods give an adsorption rate that diverges in the limit of an infinite surface.