  The question of how systems respond to perturbations is ubiquitous in
physics. Predicting this response for large classes of systems becomes
particularly challenging if many degrees of freedom are involved and linear
response theory cannot be applied. Here, we consider isolated many-body quantum
systems which either start out far from equilibrium and then thermalize, or
find themselves near thermal equilibrium from the outset. We show that
time-periodic perturbations of moderate strength, in the sense that they do not
heat up the system too quickly, give rise to the following phenomenon of
stalled response: While the driving usually causes quite considerable reactions
as long as the unperturbed system is far from equilibrium, the driving effects
are strongly suppressed when the unperturbed system approaches thermal
equilibrium. Likewise, for systems prepared near thermal equilibrium, the
response to the driving is barely noticeable right from the beginning.
Numerical results are complemented by a quantitatively accurate analytical
description and by simple qualitative arguments.
