  We discuss a new analytical approach to real-time evolution in quantum
many-body systems. Our approach extends the framework of continuous unitary
transformations such that it amounts to a novel solution method for the
Heisenberg equations of motion for an operator. It is our purpose to illustrate
the accuracy of this approach by studying dissipative quantum systems on all
time scales. In particular, we obtain results for non-equilibrium correlation
functions for general initial conditions. We illustrate our ideas for the
exactly solvable dissipative oscillator, and, as a non-trivial model, for the
dissipative two-state system.
