Quantum emission from two-dimensional black holes

We investigate Hawking radiation from two-dimensional dilatonic black holes using standard quantization techniques. In the background of a collapsing black-hole solution the Bogoliubov coefficients can be exactly determined. In the regime after the black hole has settled down to an ``equilibrium'' state but before the back reaction becomes important these give the known result of a thermal distribution of Hawking radiation at a temperature /2. The density matrix is computed in this regime and shown to be purely thermal. Similar techniques can be used to derive the stress tensor. The resulting expression agrees with the derivation based on the conformal anomaly and can be used to incorporate the back reaction. Corrections to the thermal density matrix are also examined, and it is argued that to leading order in perturbation theory the effect of the back reaction is to modify the Bogoliubov transformation, but not in a way that restores information lost to the black hole.