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

Infrared problem in quantum acoustodynamics at finite temperature