ar X iv : c on d - m at / 9 91 10 15 v 1 2 N ov 1 99 9 Effect of transport coefficients on the time - dependence of density matrix

For Lindblad's master equation of open quantum systems with a general quadratic form of the Hamiltonian, the propagator of the density matrix is analytically calculated by using path integral techniques. The time-dependent density matrix is applied to nuclear barrier penetration in heavy ion collisions with inverted oscillator and double-well potentials. The quantum mechanical decoherence of pairs of phase space histories in the propagator is studied and shown that the decoherence depends crucially on the transport coefficients.