  We show that a distinguishable mobile impurity inside a one-dimensional
many-body state at zero temperature generally does not behave like a
quasiparticle (QP). Instead, both the impurities dynamics as well as the ground
state of the bath are fundamentally transformed by a diverging number of
zero-energy excitations being generated, leading to what we call
infrared-dominated (ID) dynamics. Combining analytics and DMRG numerics we
provide a general formula for the power law governing ID dynamics at zero
momentum, discuss a threshold beyond which quasiparticle dynamics may occur
again, and study the competition between the ID and quasiparticle universality
classes at larger impurity momenta.
