Quantum non-Markovian Langevin formalism for heavy ion reactions near the Coulomb barrier

The generalized Langevin approach is suggested to describe the capture inside of the Coulomb barrier of two heavy nuclei at bombarding energies near the barrier. The equations of motion for the relative distance (collective coordinate) between two interacting nuclei are consistent with the generalized quantum fluctuation-dissipation relations. The analytical expressions are derived for the time-dependent non-Markovian microscopic transport coefficients for the stable and unstable collective modes. The calculated results show that the quantum effects in the diffusion process increase with increasing friction or/and decreasing temperature. The capture probability inside of the Coulomb barrier is enhanced by the quantum noise at low energies near the barrier. An increase of the passing probability with dissipation is found at sub-barrier energies