Schecter, Michael2014-11-032014-11-032014-08https://hdl.handle.net/11299/167460University of Minnesota Ph.D. dissertation. August 2014. Major: Physics. Advisor: Alex Kamenev. 1 computer file (PDF); vii, 96 pages.We study the dynamics of mobile impurities in a one-dimensional quantum liquid. Due to singular scattering with low-energy excitations of the host liquid, the impurity spectral properties become strongly renormalized even at weak coupling. This leads to universal phenomena with no higher-dimensional counterparts, such as lattice-free Bloch oscillations, power-law threshold behavior in the impurity spectral function and a quantum phase transition as the impurity mass exceeds a critical value. The additional possibility of integrability in one-dimension leads to the absence of thermal viscosity at special points in parameter space. The vanishing of the phonon-mediated Casimir interaction between separate impurities can be understood on the same footing. We explore these remarkable phenomena by developing an effective low-energy theory that identifies the proper collective coordinates of the dressed impurity, and their coupling to the low-energy excitations of the host liquid. The main appeal of our approach lies in its ability to describe a dynamic response using effective parameters which obey exact thermodynamic relations. The latter may be extracted using powerful numerical or analytical techniques available in one-dimension, yielding asymptotically exact results for the low-energy impurity dynamics.en1d quantum liquidsBloch oscillationsMobile impurityNon-equilibrium transportSuperfluidityUltracold atomsPhysicsThesis or Dissertation