Semiclassics for a dissipative quantum map

We present a semiclassical analysis for a dissipative quantum map with an area-nonpreserving classical limit, We show that in the limit (h) over bar --> 0 the tract of an arbitrary natural power of the propagator is dominated by contributions from periodic orbits of the corresponding classical dissipative motion. We derive trace formulae of the Gutzwiller type for such quantum maps. In comparison to Tabor's formula for area-preserving maps, both classical action and stability prefactor are modified by the dissipation. We evaluate the traces explicitly in the case of a dissipative kicked top with integrable classical motion and find good agreement with numerical results. (C) 1999 Elsevier Science B.V. All rights reserved.