  To locate the position and characterize the dynamics of a vacancy in a
crystal, we propose to represent it by the ground state density of a quantum
probe quasi-particle for the Hamiltonian associated to the potential energy
field generated by the atoms in the sample. In this description, the h^2/2mu
coefficient of the kinetic energy term is a tunable parameter controlling the
density localization in the regions of relevant minima of the potential energy
field. Based on this description, we derive a set of collective variables that
we use in rare event simulations to identify some of the vacancy diffusion
paths in a 2D crystal. Our simulations reveal, in addition to the simple and
expected nearest neighbor hopping path, a collective migration mechanism of the
vacancy. This mechanism involves several lattice sites and produces a long
range migration of the vacancy. Finally, we also observed a vacancy induced
crystal reorientation process.
