Employing the quadratic fermionic Hamiltonians for the collective and internal subsystems with a linear coupling, we studied the role of fermionic statistics on the dynamics of the collective motion. The transport coefficients are discussed as well a
s the associated fluctuation-dissipation relation. Due to different nature of the particles, the path to equilibrium is slightly affected. However, in the weak coupling regime, the time-scale for approaching equilibrium is found to be globally unchanged. The Pauli-blocking effect can modify the usual picture in open quantum system. In some limits, contrary to boson, this effect can strongly hinder the influence of the bath by blocking the interacting channels.
Various sub-barrier capture reactions with beams $^{16,18}$O and $^{40,48}$Ca are treated within the quantum diffusion approach. The role of neutron transfer in these capture reactions is discussed. The quasielastic and capture barrier distributions
are analyzed and compared with the recent experimental data.
Comparing the capture cross sections calculated without the breakup effect and experimental complete fusion cross sections, the breakup was analyzed in reactions with weakly bound projectiles $^{6,7,9}$Li, $^{9,11}$Be, and $^{6,8}$He. A trend of a sy
stematic behavior for the complete fusion suppression as a function of the target charge and bombarding energy is not achieved. The quasielastic backscattering is suggested to be an useful tool to study the behavior of the breakup probability in reactions with weakly bound projectiles.
With the quantum diffusion approach the behavior of capture cross sections and mean-square angular momenta of captured systems are revealed in the reactions with deformed nuclei at subbarrier energies. The calculated results are in a good agreement w
ith existing experimental data. With decreasing bombarding energy under the barrier the external turning point of the nucleusnucleus potential leaves the region of short-range nuclear interaction and action of friction. Because of this change of the regime of interaction, an unexpected enhancement of the capture cross section is expected at bombarding energies far below the Coulomb barrier. This effect is shown its worth in the dependence of mean-square angular momentum of captured system on the bombarding energy. From the comparison of calculated and experimental capture cross sections, the importance of quasifission near the entrance channel is shown for the actinide-based reactions leading to superheavy nuclei.
