  The singularities of the dynamical response function are one of the most
remarkable effects in many-body interacting systems. However in one dimension
these divergences only exist strictly at zero temperature, making their
observation very difficult in most cold atomic experimental settings. Moreover
the presence of a finite temperature destroys another feature of
one-dimensional quantum liquids: the real space quasi-long-range order in which
the spatial correlation functions exhibit power-law decay. We consider a
non-equilibrium protocol where two interacting Bose gases are prepared either
at different temperatures or chemical potentials and then joined. We show that
the non-equilibrium steady state emerging at large times around the junction
displays edge singularities in the response function and quasi-long-range
order.
