  We study the infrared dynamics of low-energy atoms interacting with a sample
of suspended graphene at finite temperature. The dynamics exhibits severe
infrared divergences order by order in perturbation theory as a result of the
singular nature of low-energy flexural phonon emission. Our model can be viewed
as a two-channel generalization of the independent boson model with asymmetric
atom-phonon coupling. This allows us to take advantage of the exact
non-perturbative solution of the independent boson model in the stronger
channel while treating the weaker one perturbatively. In the low-energy limit,
the exact solution can be viewed as a resummation (exponentiation) of the most
divergent diagrams in the perturbative expansion. As a result of this
procedure, we obtain the atom's Green function which we use to calculate the
atom damping rate, a quantity equal to the quantum sticking rate. A
characteristic feature of our results is that the Green's function retains a
weak, infrared cutoff dependence that reflects the reduced dimensionality of
the problem. As a consequence, we predict a measurable dependence of the
sticking rate on graphene sample size. We provide detailed predictions for the
sticking rate of atomic hydrogen as a function of temperature and sample size.
The resummation yields an enhanced sticking rate relative to the conventional
Fermi golden rule result (equivalent to the one-loop atom self-energy), as
higher-order processes increase damping at finite temperature.
