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We show that a distinguishable mobile impurity inside a one-dimensionalmany-body state at zero temperature generally does not behave like aquasiparticle (QP). Instead, both the impurities dynamics as well as the groundstate of the bath are fundamentally transformed by a diverging number ofzero-energy excitations being generated, leading to what we callinfrared-dominated (ID) dynamics. Combining analytics and DMRG numerics weprovide a general formula for the power law governing ID dynamics at zeromomentum, discuss a threshold beyond which quasiparticle dynamics may occuragain, and study the competition between the ID and quasiparticle universalityclasses at larger impurity momenta.

Competing regimes of motion in 1D mobile impurities