Time-dependent description of heavy-ion collisions

In this thesis, we aim to advance the time-dependent transport theories for the description of heavy-ion collisions, from two perspectives. As an attempt to address multifragmentation in nuclear collisions, we develop a stochastic transport model based on one-body Langevin dynamics. The new model is subsequently tested and benchmarked with a series of other existing models with satisfaction. The model is also applied to address and confirm the so-called "hierarchy effect" observed in the multifragmentation for certain systems around Fermi energies. Parallel to the development towards a stochastic theory, we also extend an approach based on non-equilibrium Green's function for the description of correlated nuclear systems in one dimension.Firstly, we present a new framework to treat the dissipation and fluctuation dynamics associated with nucleon-nucleon scattering in heavy-ion collisions. The two-body collisions are effectively described in terms of the diffusion of nucleons in viscous nuclear media, governed by a set of Langevin equations in momentum space. The new framework combined with the usual mean-field dynamics, forming the basis of the new stochastic model, can be used to simulate heavy-ion collisions at intermediate energies.Subsequently, as a proof of principle for the new model, we simulate Au + Au reactions 100 MeV/nucleon and at 400 MeV/nucleon and look at observables such as rapidity distribution and flow as a function of rapidity. The results are found to be consistent with other existing models under the same constrained conditions. To demonstrate the model's ability to describe multifragmentation, we also study the formation of fragments in Sn +Sn reactions at 50 MeV/nucleon, and the fragment distribution and properties are discussed and compared to two other models commonly employed for collisions.Next, we move on to tackle the "hierarchy effect" observed experimentally for reactions around Fermi energies. We simulate Ta + Au at 39.6 MeV/nucleon and compare mainly the charge and velocity distributions of the fragments from the QP with experimental data. Our simulation results can reproduce the trends observed in data, and a semi-quantitative agreement can be reached. This is the first time, to our knowledge, that one has succeeded in addressing the "hierarchy effect" with a dynamic model. The simulation of U + C is also discussed.Finally, we present a fully quantum-mechanical model based on non-equilibrium Green's function, with short-range two-body correlations incorporated as an extension. We examine its applications to one-dimensional nuclear systems, such as the preparation and properties of the ground states, the isovector oscillation of symmetric systems and the boosting of a"slab" in a periodic box. In particular, the dissipation brought by two-body correlations and the Galilean covariance of the theory are demonstrated. These studies lay the groundwork for the future exploration of collisions of correlated nuclear systems in one dimension.