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Quenched dynamics in interacting one-dimensional systems: Appearance of current carrying steady states from initial domain wall density profiles

We investigate dynamics arising after an interaction quench in the quantum sine-Gordon model for a one-dimensional system initially prepared in a spatially inhomogeneous domain wall state. We study the time-evolution of the density, current and equal time correlation functions using the truncated Wigner approximation (TWA) to which quantum corrections are added in order to set the limits on its validity. For weak to moderate strengths of the back-scattering interaction, the domain wall spreads out ballistically with the system within the light cone reaching a nonequilibrium steady-state characterized by a net current flow. A steady state current exists for a quench at the exactly solvable Luther-Emery point. The magnitude of the current decreases with increasing strength of the back-scattering interaction. The two-point correlation function of the variable canonically conjugate to the density reaches a spatially oscillating steady state at a wavelength inversely related to the current.