Coherent state propagation in open systems

We introduce the generalized coherent states (G.C.S.) as eigenstates of the unitarily equivalent representations of the annihilation operator. The G.C.S. extension in phase space evolves with time and keeps the uncertainly product (with correlation) at its minimum. The conditions for the propagation of the G.C.S. in a time-dependent field are derived. In the presence of dissipation, an equation of motion is found that describes the G.C.S. decay towards the ground state; its results are compared with those of non-linear Schrödinger equations.