Quantum tunneling with dissipation in smoothly joined parabolic potential

This paper is devoted to the study of quantum dissipation in cluster decay phenomena in the frame of the Lindblad approach to quantum open systems. The tunneling of a metastable state across a piecewise quadratic potential is envisaged for two cases : one and two harmonic wells smoothly joined to an inverted parabola which simulates the barrier. The width and depth of the second harmonic oscillator well was varied over a wide range of values in order to encompass particular cases of tunneling such as the double well potential and the cluster decay. The evolution of the averages and covariances of the quantum sub-system is studied in both under- and overdamped regimes. For a gaussian intial wave-packet we compute the tunneling probability for different values of the friction coefficient and fixed values of the diffusion coefficients.