  We review a molecular dynamics method for nucleon many-body systems called
the quantum molecular dynamics (QMD) and our studies using this method. These
studies address the structure and the dynamics of nuclear matter relevant to
the neutron star crusts, supernova cores, and heavy-ion collisions. A key
advantage of QMD is that we can study dynamical processes of nucleon many-body
systems without any assumptions on the nuclear structure. First we focus on the
inhomogeneous structures of low-density nuclear matter consisting not only of
spherical nuclei but also of nuclear "pasta", i.e., rod-like and slab-like
nuclei. We show that the pasta phases can appear in the ground and equilibrium
states of nuclear matter without assuming nuclear shape. Next we show our
simulation of compression of nuclear matter which corresponds to the collapsing
stage of supernovae. With increase of density, a crystalline solid of spherical
nuclei change to a triangular lattice of rods by connecting neighboring nuclei.
Finally, we discuss the fragment formation in expanding nuclear matter. Our
results suggest that a generally accepted scenario based on the liquid-gas
phase transition is not plausible at lower temperatures.
