Exact Results in Quantum Theory

The singularities of the dynamical response function are one of the most remarkable effects in many-body critical one-dimensional systems. However these divergences exists only strictly at zero temperature. I will show that by joining two interacting Bose gases prepared either at different temperatures or chemical potentials, the non-equilibrium steady state (ness) emerging at large times around the junction displays edge singularities in the response function and quasi-long range order as would be expected for a critical ground state.