Effect of transport coefficients on the time dependence of a density matrix

For Lindblad's master equation of open quantum systems with the Hamiltonian in a general quadratic form, the propagator of the density matrix is calcu lated analytically by using pathintegral techniques. The time-dependent den sity matrix is applied to nuclear barrier penetration in heavy ion collisio ns with inverted oscillator and double-well potentials. The quantum mechani cal decoherence of pairs of phase space histories in the propagator is stud ied and it is shown that the decoherence depends crucially on the transport coefficients.