A simplified derivation of stimulated emission by black holes

A black hole, when acting as a scatterer for quanta in a single mode of a massless scalar field, is known to convert any ingoing Gibbs state of that mode into an outgoing Gibbs state (with some other mean particle number). The paper presents a simple derivation for this property which may help to clarify what relation, if any, it bears to the microscopic structure of the black hole horizon.