DISSIPATIVE QUANTUM-SYSTEMS WITH A POTENTIAL BARRIER .2. DYNAMICS NEAR THE BARRIER TOP

We study the real time dynamics of a quantum system with a potential b arrier coupled to a heat-bath environment. The time evolution of the d ensity matrix starting from a general initial state is evaluated expli citly in the semiclassical approximation. As the temperature is decrea sed below a critical temperature T-c, large quantum fluctuations rende r the harmonic approximation near the barrier top insufficient and a c austic arises. As a consequence, anharmonicities of the potential beco me essential even in the close vicinity of the barrier top and the sem iclassical density matrix has to be evaluated beyond the Gaussian appr oximation. The range of validity with respect to temperature and time of the semiclassical analytical results is discussed in detail. We ill ustrate the outcome of the theory with an explicit example.