Infrared problem in quantum acoustodynamics at finite temperature

TL;DR

This paper analytically investigates the infrared divergence issues in quantum acoustodynamics at finite temperature, revealing that phonon emission suppresses atom sticking probability on elastic membranes.

Contribution

It introduces a coherent state basis approach to resolve infrared divergences and provides explicit formulas showing exponential suppression of atom sticking at finite temperature.

Findings

Infrared divergences are mitigated using a coherent state phonon basis.

Sticking probability vanishes exponentially with membrane size at finite temperature.

Soft phonon emission does not restore atom sticking probability at nonzero temperature.

Abstract

The phonon-assisted sticking rate of slow moving atoms impinging on an elastic membrane at nonzero temperature is studied analytically using a model with linear atom-phonon interactions, valid in the weak coupling regime. A perturbative expansion of the adsorption rate in the atom-phonon coupling is infrared divergent at zero temperature, and this infrared problem is exacerbated by finite temperature. The use of a coherent state phonon basis in the calculation, however, yields infrared-finite results even at finite temperature. The sticking probability with the emission of any finite number of phonons is explicitly seen to be exponentially small, and it vanishes as the membrane size grows, a result that was previously found at zero temperature; in contrast to the zero temperature case, this exponential suppression of the sticking probability persists even with the emission of an infinite number of soft phonons. Explicit closed-form expressions are obtained for the effects of soft-phonon emission at finite temperature on the adsorption rate. For slowly moving atoms, the model predicts that there is zero probability of sticking to a large elastic membrane at nonzero temperature and weak coupling.