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Nucleon exchange mechanism is investigated in central collisions of symmetric heavy-ions in the basis of the stochastic mean-field approach. Quantal diffusion coefficients for nucleon exchange are calculated by including non-Markovian effects and shell structure.

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In order to describe the fusion of two very heavy nuclei at near barrier energies, a generalized Langevin approach is proposed, which incorporates the quantum statistical fluctuations in accordance with the fluctuation and dissipation theorem. It is illustrated that the quantum statistical effects introduce an enhancement of the formation of compound nucleus, though the quantum enhancement is somewhat less pronounced as indicated in the previous calculations.

Quantal effects on growth of spinodal instabilities in charge asymmetric nuclear matter are investigated in the framework of a stochastic mean field approach. Due to quantal effects, in both symmetric and asymmetric matter, dominant unstable modes shift towards longer wavelengths and modes with wave numbers larger than the Fermi momentum are strongly suppressed. As a result of quantum statistical effects, in particular at lower temperatures, magnitude of density fluctuations grows larger than those calculated in semi-classical approximation.