Quantum electrodynamics (QED) provides a highly accurate description of phenomena
involving the interaction of atoms with light. We argue that the quantum theory describing the
interaction of cold atoms with a vibrating membrane—quantum acoustodynamics (QAD)—
shares many issues and features with QED. Specifically, the adsorption of an atom on a
vibrating membrane can be viewed as the counterpart to QED radiative electron capture. A
calculation of the adsorption rate to lowest order in the atom-phonon coupling is finite; …

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 …