Non-minimal scalar fields in 2D de Sitter and dilaton black holes

We study non-minimal quantum fields in the gravitational field of 2-dimensional dilaton black holes and the de Sitter spacetime. We found that the Green functions for non-minimal massless fields in a particular class of dilaton black holes and in the de Sitter spacetime are almost identical. Using this symmetry exact solutions are derived for quasinormal modes and bound states in these background geometries. The problem of stability of dilaton black holes is discussed.