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Using the quantum trajectories approach we study the quantum dynamics of adissipative chaotic system described by the Zaslavsky map. For strongdissipation the quantum wave function in the phase space collapses onto acompact packet which follows classical chaotic dynamics and whose area isproportional to the Planck constant. At weak dissipation the exponentialinstability of quantum dynamics on the Ehrenfest time scale dominates and leadsto wave packet explosion. The transition from collapse to explosion takes placewhen the dissipation time scale exceeds the Ehrenfest time. For integrablenonlinear dynamics the explosion practically disappears leaving place tocollapse.Comment: 4 pages, 4 figure

Dissipative Quantum Chaos: Transition from Wave Packet Collapse to Explosion